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This classic problem asks us to find the critical launch angle 'theta' at which the range R is maximum (horizontal distance of landing point measured from the foot of the tower). I could think of 3 separate methods for solving this. Please let me know in comments if you can think of another method. ARVIND CHAUHAN'S ONLINE PHYSICS ACADEMY B. Tech., IIT-Kanpur, India; MBA, Canada; MSc, England Please like and subscribe to my channel to learn advanced techniques for solving difficult Physics problems. Visit https://www.arvindchauhan.com/ to register for exam prep courses. I am an Aerospace Engineer, Entrepreneur & Educator, and have been teaching Physics and Applied Calculus for IIT JEE, AIIMS, NEET, SAT, Olympiads and other college entrance exams since 1993. My best result was in 2006, when my students studying in my regular 2 year classroom program at my coaching "PI Scholastics" in Chandigarh, bagged All India JEE Advanced Ranks 1, 4, 6 & 7 in general category (FROM THE SAME BATCH) - a feat which, respectfully, no other teacher or coaching institute has ever been able to beat! My past results – All India Ranks in JEE Advanced, General Category: Rank 1: Raghu Mahajan, JEE 2006 Rank 2: Amit Agarwal, JEE 1999 Rank 4: Kashish Mittal, JEE 2006 Rank 4: Archit Gupta, JEE 2008 Rank 5: Ankur Goel, JEE 2004 Rank 6: Prateek Mittal, JEE 2006 Rank 6: Ankit Garg, JEE 2007 Rank 6: Trinabh Gupta, JEE 2005 Rank 7: Rushil Goel, JEE 2006 Rank 7: Adish Singla, JEE 2001 Rank 8: Vikas Bansal, JEE 1999 Rank 9: Ankit Jain, JEE 2003 Rank 10: Dhruv Mahajan, JEE 2000 Rank 10: Ashish Gupta, JEE 1998 Rank 11: Movin Jain, JEE 2005 Rank 13: Mohit Mittal, JEE 1996 Rank 20: Kunal Mittal, JEE 2015 Rank 27: Abhijit Lavania, JEE 2013 Rank 28: Binny Bansal, JEE 2001 Rank 30: Aastha Jain, IIT-JEE 2000 #jeeadvancedphysics #jeeadvanced #jeemainsphysics #physicsproblems #jeepreparation
Maximum range of a projectile fired from a tower
This is a clip from a live class in which we analyze the locus of a cycloid in rotational kinematics, as well as the case of a charged particle moving along a cycloid locus in a special region of electric and magnetic fields. Language is "hinglish". ARVIND CHAUHAN'S ONLINE PHYSICS ACADEMY B. Tech., IIT-Kanpur, India; MBA, Canada; MSc, England Please like and subscribe to my channel to learn advanced techniques for solving difficult Physics problems. Visit https://www.arvindchauhan.com/ to register for exam prep courses. I am an Aerospace Engineer, Entrepreneur & Educator, and have been teaching Physics and Applied Calculus for IIT JEE, AIIMS and other college entrance exams since 1993. My best result was in 2006, when my students studying in my regular 2 year classroom program at my coaching "PI Scholastics" in Chandigarh, bagged All India JEE Advanced Ranks 1, 4, 6 & 7 in general category (FROM THE SAME BATCH) - a feat which, respectfully, no other teacher or coaching institute has ever been able to beat! My past results – All India Ranks in JEE Advanced, General Category: Rank 1: Raghu Mahajan, JEE 2006 Rank 2: Amit Agarwal, JEE 1999 Rank 4: Kashish Mittal, JEE 2006 Rank 4: Archit Gupta, JEE 2008 Rank 5: Ankur Goel, JEE 2004 Rank 6: Prateek Mittal, JEE 2006 Rank 6: Ankit Garg, JEE 2007 Rank 6: Trinabh Gupta, JEE 2005 Rank 7: Rushil Goel, JEE 2006 Rank 7: Adish Singla, JEE 2001 Rank 8: Vikas Bansal, JEE 1999 Rank 9: Ankit Jain, JEE 2003 Rank 10: Dhruv Mahajan, JEE 2000 Rank 10: Ashish Gupta, JEE 1998 Rank 11: Movin Jain, JEE 2005 Rank 13: Mohit Mittal, JEE 1996 Rank 20: Kunal Mittal, JEE 2015 Rank 27: Abhijit Lavania, JEE 2013 Rank 28: Binny Bansal, JEE 2001 Rank 30: Aastha Jain, IIT-JEE 2000 #jeeadvancedphysics #jeeadvanced #jeemainsphysics #physicsproblems #jeepreparation
Cycloid Locus in Pure Rolling and Magnetism - JEE Advanced Physics
This video clip from a live class talks about how area charge density 'sigma' is defined and an example of a hemispherical surface charge is discussed, for finding the electric field using integration. ARVIND CHAUHAN'S ONLINE PHYSICS ACADEMY B. Tech., IIT-Kanpur, India; MBA, Canada; MSc, England Please like and subscribe to my channel to learn advanced techniques for solving difficult Physics problems. Visit https://www.arvindchauhan.com/ to register for exam prep courses. I am an Aerospace Engineer, Entrepreneur & Educator, and have been teaching Physics and Applied Calculus for IIT JEE, AIIMS and other college entrance exams since 1993. My best result was in 2006, when my students studying in my regular 2 year classroom program at my coaching "PI Scholastics" in Chandigarh, bagged All India JEE Advanced Ranks 1, 4, 6 & 7 in general category (FROM THE SAME BATCH) - a feat which, respectfully, no other teacher or coaching institute has ever been able to beat! My past results – All India Ranks in JEE Advanced, General Category: Rank 1: Raghu Mahajan, JEE 2006 Rank 2: Amit Agarwal, JEE 1999 Rank 4: Kashish Mittal, JEE 2006 Rank 4: Archit Gupta, JEE 2008 Rank 5: Ankur Goel, JEE 2004 Rank 6: Prateek Mittal, JEE 2006 Rank 6: Ankit Garg, JEE 2007 Rank 6: Trinabh Gupta, JEE 2005 Rank 7: Rushil Goel, JEE 2006 Rank 7: Adish Singla, JEE 2001 Rank 8: Vikas Bansal, JEE 1999 Rank 9: Ankit Jain, JEE 2003 Rank 10: Dhruv Mahajan, JEE 2000 Rank 10: Ashish Gupta, JEE 1998 Rank 11: Movin Jain, JEE 2005 Rank 13: Mohit Mittal, JEE 1996 Rank 20: Kunal Mittal, JEE 2015 Rank 27: Abhijit Lavania, JEE 2013 Rank 28: Binny Bansal, JEE 2001 Rank 30: Aastha Jain, IIT-JEE 2000 #jeeadvancedphysics #jeeadvanced #jeemainsphysics #physicsproblems #jeepreparation #surfacechargedensity #electricfield #hemisphere
Electric field due to a hemisphere carrying uniform charge of density 'sigma' on its curved surface
Calculate the Force required to hold a chain of mass M and length = radius of Earth, which is hanging inside a tunnel through Earth's diameter. This Force's value can be thought of as being equal to the 'weight' of the chain! ARVIND CHAUHAN'S ONLINE PHYSICS ACADEMY B. Tech., IIT-Kanpur, India; MBA, Canada; MSc, England Please like and subscribe to my channel to learn advanced techniques for solving difficult Physics problems. Visit https://www.arvindchauhan.com/ to register for exam prep courses. I am an Aerospace Engineer, Entrepreneur & Educator, and have been teaching Physics and Applied Calculus for IIT JEE, AIIMS and other college entrance exams since 1993. My best result was in 2006, when my students studying in my regular 2 year classroom program at my coaching "PI Scholastics" in Chandigarh, bagged All India JEE Advanced Ranks 1, 4, 6 & 7 in general category (FROM THE SAME BATCH) - a feat which, respectfully, no other teacher or coaching institute has ever been able to beat! My past results – All India Ranks in JEE Advanced, General Category: Rank 1: Raghu Mahajan, JEE 2006 Rank 2: Amit Agarwal, JEE 1999 Rank 4: Kashish Mittal, JEE 2006 Rank 4: Archit Gupta, JEE 2008 Rank 5: Ankur Goel, JEE 2004 Rank 6: Prateek Mittal, JEE 2006 Rank 6: Ankit Garg, JEE 2007 Rank 6: Trinabh Gupta, JEE 2005 Rank 7: Rushil Goel, JEE 2006 Rank 7: Adish Singla, JEE 2001 Rank 8: Vikas Bansal, JEE 1999 Rank 9: Ankit Jain, JEE 2003 Rank 10: Dhruv Mahajan, JEE 2000 Rank 10: Ashish Gupta, JEE 1998 Rank 11: Movin Jain, JEE 2005 Rank 13: Mohit Mittal, JEE 1996 Rank 20: Kunal Mittal, JEE 2015 Rank 27: Abhijit Lavania, JEE 2013 Rank 28: Binny Bansal, JEE 2001 Rank 30: Aastha Jain, IIT-JEE 2000 #jeeadvancedphysics #jeeadvanced #jeemainsphysics #physicsproblems #jeepreparation #earthsgravity #tunnelthroughearth #earth #irodov
Weight of a chain hanging inside a tunnel through Earth's diameter
If Earth cools would a day become smaller due to thermal contraction and conservation of angular momentum. As earth cools and contracts, its moment of inertia decreases thus increasing its angular velocity of rotation, which will reduce a day's duration from 24 hours to some minutes less than 24 hours! ARVIND CHAUHAN'S ONLINE PHYSICS ACADEMY B. Tech., IIT-Kanpur, India; MBA, Canada; MSc, England Please like and subscribe to my channel to learn advanced techniques for solving difficult Physics problems. Visit https://www.arvindchauhan.com/ to register for exam prep courses. I am an Aerospace Engineer, Entrepreneur & Educator, and have been teaching Physics and Applied Calculus for IIT JEE, AIIMS and other college entrance exams since 1993. My best result was in 2006, when my students studying in my regular 2 year classroom program at my coaching "PI Scholastics" in Chandigarh, bagged All India JEE Advanced Ranks 1, 4, 6 & 7 in general category (FROM THE SAME BATCH) - a feat which, respectfully, no other teacher or coaching institute has ever been able to beat! My past results – All India Ranks in JEE Advanced, General Category: Rank 1: Raghu Mahajan, JEE 2006 Rank 2: Amit Agarwal, JEE 1999 Rank 4: Kashish Mittal, JEE 2006 Rank 4: Archit Gupta, JEE 2008 Rank 5: Ankur Goel, JEE 2004 Rank 6: Prateek Mittal, JEE 2006 Rank 6: Ankit Garg, JEE 2007 Rank 6: Trinabh Gupta, JEE 2005 Rank 7: Rushil Goel, JEE 2006 Rank 7: Adish Singla, JEE 2001 Rank 8: Vikas Bansal, JEE 1999 Rank 9: Ankit Jain, JEE 2003 Rank 10: Dhruv Mahajan, JEE 2000 Rank 10: Ashish Gupta, JEE 1998 #jeeadvancedphysics #jeeadvanced #jeemainsphysics #physicsproblems #jeepreparation #earthrotation #durationofday
If Earth cools would a day become smaller?
Calculate the Electric field on the axis of a long half cylinder, whose surface carries a charge of uniform area density sigma. ARVIND CHAUHAN'S ONLINE PHYSICS ACADEMY B. Tech., IIT-Kanpur, India; MBA, Canada; MSc, England Please like and subscribe to my channel to learn advanced techniques for solving difficult Physics problems. Visit https://www.arvindchauhan.com/ to register for exam prep courses. I am an Aerospace Engineer, Entrepreneur & Educator, and have been teaching Physics and Applied Calculus for IIT JEE, AIIMS and other college entrance exams since 1993. My best result was in 2006, when my students studying in my regular 2 year classroom program at my coaching "PI Scholastics" in Chandigarh, bagged All India JEE Advanced Ranks 1, 4, 6 & 7 in general category (FROM THE SAME BATCH) - a feat which, respectfully, no other teacher or coaching institute has ever been able to beat! My past results – All India Ranks in JEE Advanced, General Category: Rank 1: Raghu Mahajan, JEE 2006 Rank 2: Amit Agarwal, JEE 1999 Rank 4: Kashish Mittal, JEE 2006 Rank 4: Archit Gupta, JEE 2008 Rank 5: Ankur Goel, JEE 2004 Rank 6: Prateek Mittal, JEE 2006 Rank 6: Ankit Garg, JEE 2007 Rank 6: Trinabh Gupta, JEE 2005 Rank 7: Rushil Goel, JEE 2006 Rank 7: Adish Singla, JEE 2001 Rank 8: Vikas Bansal, JEE 1999 Rank 9: Ankit Jain, JEE 2003 Rank 10: Dhruv Mahajan, JEE 2000 Rank 10: Ashish Gupta, JEE 1998 #jeeadvancedphysics #jeeadvanced #jeemainsphysics #physicsproblems #jeepreparation #electricfield #half-cylinder
Electric field due to half cylindrical surface charge
2 moles of a mono-atomic ideal gas is enclosed in a vertical cylinder fitted with a piston of weight 200 N and cross-sectional area 20 square centimetres. The cylinder walls and the piston are heat insulating. The piston is connected to a vertical spring of spring constant 200 N/m. Initially the temperature of the gas is 300 K and the spring is in its natural length. The atmospheric pressure above the piston is 100 kPa. The gas is heated slowly by means of an electric heater so that the piston moves up slowly by 50 cm. What is the total heat supplied to the gas, by the heater, during this process? ARVIND CHAUHAN'S ONLINE PHYSICS ACADEMY B. Tech., IIT-Kanpur, India; MBA, Canada; MSc, England Please like and subscribe to my channel to learn advanced techniques for solving difficult Physics problems. Visit https://www.arvindchauhan.com/ to register for exam prep courses. I am an Aerospace Engineer, Entrepreneur & Educator, and have been teaching Physics and Applied Calculus for IIT JEE, AIIMS and other college entrance exams since 1993. My best result was in 2006, when my students studying in my regular 2 year classroom program at my coaching "PI Scholastics" in Chandigarh, bagged All India JEE Advanced Ranks 1, 4, 6 & 7 in general category (FROM THE SAME BATCH) - a feat which, respectfully, no other teacher or coaching institute has ever been able to beat! My past results – All India Ranks in JEE Advanced, General Category: Rank 1: Raghu Mahajan, JEE 2006 Rank 2: Amit Agarwal, JEE 1999 Rank 4: Kashish Mittal, JEE 2006 Rank 4: Archit Gupta, JEE 2008 Rank 5: Ankur Goel, JEE 2004 Rank 6: Prateek Mittal, JEE 2006 Rank 6: Ankit Garg, JEE 2007 Rank 6: Trinabh Gupta, JEE 2005 Rank 7: Rushil Goel, JEE 2006 Rank 7: Adish Singla, JEE 2001 Rank 8: Vikas Bansal, JEE 1999 Rank 9: Ankit Jain, JEE 2003 Rank 10: Dhruv Mahajan, JEE 2000 Rank 10: Ashish Gupta, JEE 1998 Rank 11: Movin Jain, JEE 2005 Rank 13: Mohit Mittal, JEE 1996 Rank 20: Kunal Mittal, JEE 2015 Rank 27: Abhijit Lavania, JEE 2013 Rank 28: Binny Bansal, JEE 2001 Rank 30: Aastha Jain, IIT-JEE 2000 #jeeadvancedphysics #jeeadvanced #jeemainsphysics #physicsproblems #jeepreparation
Gas being heated, piston pushed up compressing the spring - a classic thermodynamics problem
In a spring-mass-damper oscillatory system, the mass of the block is 2 kg, spring constant is 20 N/m and the damping coefficient b equals 4 kg/s. We are asked to find the time period of damped oscillations (integer type question). ARVIND CHAUHAN'S ONLINE PHYSICS ACADEMY B. Tech., IIT-Kanpur, India; MBA, Canada; MSc, England Please like and subscribe to my channel to learn advanced techniques for solving difficult Physics problems. Visit https://www.arvindchauhan.com/ to register for exam prep courses. I am an Aerospace Engineer, Entrepreneur & Educator, and have been teaching Physics and Applied Calculus for IIT JEE, AIIMS and other college entrance exams since 1993. My best result was in 2006, when my students studying in my regular 2 year classroom program at my coaching "PI Scholastics" in Chandigarh, bagged All India JEE Advanced Ranks 1, 4, 6 & 7 in general category (FROM THE SAME BATCH) - a feat which, respectfully, no other teacher or coaching institute has ever been able to beat! My past results – All India Ranks in JEE Advanced, General Category: Rank 1: Raghu Mahajan, JEE 2006 Rank 2: Amit Agarwal, JEE 1999 Rank 4: Kashish Mittal, JEE 2006 Rank 4: Archit Gupta, JEE 2008 Rank 5: Ankur Goel, JEE 2004 Rank 6: Prateek Mittal, JEE 2006 Rank 6: Ankit Garg, JEE 2007 Rank 6: Trinabh Gupta, JEE 2005 Rank 7: Rushil Goel, JEE 2006 Rank 7: Adish Singla, JEE 2001 Rank 8: Vikas Bansal, JEE 1999 Rank 9: Ankit Jain, JEE 2003 Rank 10: Dhruv Mahajan, JEE 2000 Rank 10: Ashish Gupta, JEE 1998 Rank 11: Movin Jain, JEE 2005 Rank 13: Mohit Mittal, JEE 1996 Rank 20: Kunal Mittal, JEE 2015 Rank 27: Abhijit Lavania, JEE 2013 Rank 28: Binny Bansal, JEE 2001 Rank 30: Aastha Jain, IIT-JEE 2000 #jeeadvancedphysics #jeeadvanced #jeemainsphysics #physicsproblems #jeepreparation
Damped oscillations problem
Two vertical rectangular plastic plates are kept parallel to each other and submerged partially in water. The gap between them is small and equal to 𝛿. The horizontal length of each plate (measured perpendicularly into the plane of the diagram) is L. Take surface tension of water = S, and its density = 𝜌. Acceleration due to gravity is g. Considering forces of surface tension and their effect, what horizontal force F should be applied on each plate in order to hold the plates in this position? Assume contact angle of water with this special plastic is Zero, and appropriate forces are applied in the vertical direction to keep the system in equilibrium. ARVIND CHAUHAN'S ONLINE PHYSICS ACADEMY B. Tech., IIT-Kanpur, India; MBA, Canada; MSc, England Please like and subscribe to my channel to learn advanced techniques for solving difficult Physics problems. Visit https://www.arvindchauhan.com/ to register for exam prep courses. I am an Aerospace Engineer, Entrepreneur & Educator, and have been teaching Physics and Applied Calculus for IIT JEE, AIIMS and other college entrance exams since 1993. My best result was in 2006, when my students studying in my regular 2 year classroom program at my coaching "PI Scholastics" in Chandigarh, bagged All India JEE Advanced Ranks 1, 4, 6 & 7 in general category (FROM THE SAME BATCH) - a feat which, respectfully, no other teacher or coaching institute has ever been able to beat! My past results – All India Ranks in JEE Advanced, General Category: Rank 1: Raghu Mahajan, JEE 2006 Rank 2: Amit Agarwal, JEE 1999 Rank 4: Kashish Mittal, JEE 2006 Rank 4: Archit Gupta, JEE 2008 Rank 5: Ankur Goel, JEE 2004 Rank 6: Prateek Mittal, JEE 2006 Rank 6: Ankit Garg, JEE 2007 Rank 6: Trinabh Gupta, JEE 2005 Rank 7: Rushil Goel, JEE 2006 Rank 7: Adish Singla, JEE 2001 Rank 8: Vikas Bansal, JEE 1999 Rank 9: Ankit Jain, JEE 2003 Rank 10: Dhruv Mahajan, JEE 2000 Rank 10: Ashish Gupta, JEE 1998 Rank 11: Movin Jain, JEE 2005 Rank 13: Mohit Mittal, JEE 1996 Rank 20: Kunal Mittal, JEE 2015 Rank 27: Abhijit Lavania, JEE 2013 Rank 28: Binny Bansal, JEE 2001 Rank 30: Aastha Jain, IIT-JEE 2000 #jeeadvancedphysics #jeeadvanced #jeemainsphysics #physicsproblems #jeepreparation
Force of attraction between two vertical plates immersed in a liquid, due to surface tension
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