A ball is thrown up with a certain velocity at an angle $\theta$ to the horizontal. The kinetic energy $KE$ of the ball varies with horizontal displacement $x$ as

A bullet of mass $50 \mathrm{~g}$ is fired with a speed $100 \mathrm{~m} / \mathrm{s}$ on a plywood and emerges with $40 \mathrm{~m} / \mathrm{s}$. The percentage loss of kinetic energy is :

A body initially at rest, breaks up into two pieces of masses $2 M$ and $3 M$ respectively, together having a total kinetic energy $E$. The piece of mass $2 M$, after breaking up, has a kinetic energy

If the linear momentum is increased by $5\%$, the kinetic energy will increase by.......$\%$

A block of mass $m$ is sliding on a fixed frictionless concave surface of radius $R$. It is released from rest at point $P$ which is at a height of $H \ll R$ from the lowest point $Q .$

$(a)$ What is the potential energy as a function of $\theta$, taking the lowest point $Q$ as the reference level for potential energy?

$(b)$ What is the kinetic energy as a function of $\theta$ ?

$(c)$ What is the time takes for the particle to reach from point $P$ to the lowest point $Q$ ?

$(d)$ How much force is exerted by the block on the concave surface at the point $Q$ ?

A light and a heavy body have equal kinetic energy. Which one has a greater momentum ?