Question

A projectile of mass m is moving in the vertical x-y plane with the origin on the ground and y-axis pointing vertically up. Taking the gravitational potential energy to be zero on the ground, the total energy of the particle written in planar polar coordinates (r, θ) is (here g is the acceleration due to gravity)

• A. $\frac{m}{2}ṙ^2+mgr\sin\theta$
• B. $\frac{m}{2}(ṙ^2+r^2\dot\theta^2)+mgr\cos\theta$
• C. $\frac{m}{2}(ṙ^2+r^2\dot\theta^2)+mgr\sin\theta$
• D. $\frac{m}{2}(ṙ^2+r^2\dot\theta^2)-mgr\cos\theta$

Answer 1

Answer: (C)

$\frac{m}{2}(ṙ^2+r^2\dot\theta^2)+mgr\sin\theta$

Answer 2

The correct option is (C) : $\frac{m}{2}(ṙ^2+r^2\dot\theta^2)+mgr\sin\theta$.