A small ball attached to a massless string is undergoing vertical circular motion. At the highest point of its trajectory, the tension in the string is zero. Which of the following statements is TRUE about the ball's mechanical energy as it moves from the highest point to the lowest point in the circle?

A cricket ball is hit at ${30^0}$ with the horizontal with kinetric energy ${E_k}$. What is the kinetic energy at the highest point?

From a building two balls A to B are thrown such that A is thrown upwards and B downwards (both vertically). If ${v_A}$ and ${v_B}$ are their respective velocities on reaching the ground, then

If a long spring is stretched by 0.02 m, its potential energy is U. If the spring is stretched by 0.1 m, then its potential energy will be

A ball is projected vertically down with an initial velocity from a height of 20 m onto a horizontal floor. During the impact it loses $50\%$ of its energy and rebounds to the same height. The initial velocity of its projection is

A particle is subjected to a conservative force whose potential energy is given by $U(x) = ax^2 - bx^3$, where 'a' and 'b' are positive constants. At what value of 'x' is the particle in stable equilibrium?

A spring of force constant 'k' is compressed by a distance 'x' and used to launch a block of mass 'm' up a frictionless incline of angle $heta$. What is the maximum distance 'd' the block travels along the incline before momentarily coming to rest?

A particle is released from a height S.At certain height its kinetic energy is three times its potential energy .The height and speed of the particle at that instant are respectively

A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10,000 N/m. The spring compresses by

If the water falls from a dam into a turbine wheel 19.6 m below, then the velocity of water at the turbine is ($g = 9.8\;m/{s^2}$)

If a body of mass 200 g falls from a height 200 m and its total P.E. is converted into K.E. at the point of contact of the body with earth surface, then what is the decrease in P.E. of the body at the contact ($g = 10\;m/{s^2}$)