Starting from rest on her swing at initial height $h_0$ above the ground, Saina swings forward. At the lowest point of her motion, she grabs her bag that lies on the ground. Saina continues swinging forward to reach maximum height $h_1$ . She then swings backward and when reaching the lowest point of motion again, she simple lets go off the bag, which falls freely. Saina's backward swing then reaches maximum height $h_2$ . Neglecting air resistance, how are the three heights related?

Write the equation of total mechanical energy of body of mass $m$ falls freely from height $H$.

An ice block is melting at a constant rate $\left| {\,\frac{{dm}}{{dt}}\,} \right|= \mu$ . Its initial mass is $m_0$ and it is moving with velocity on a frictionless horizontal surface. The distance travelled by it till it melts completely is :

A particle of mass $m$ moving horizontally with $v_0$ strikes $a$ smooth wedge of mass $M$, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to $a$ height $h$. The maximum height h attained by the particle is 

A simple pendulum with bob of mass $m$ and length $x$ is held in position at an angle $\theta_1$ and then angle $\theta_2$ with the vertical. When released from these positions, speeds with which it passes the lowest positions are $v_1$ and $v_2$ respectively. Then, $\frac{v_1}{v_2}$ is .............

Two balls at same temperature collide. What is conserved