If the kinetic energy of a body becomes four times of its initial value, then new momentum will

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 particle of mass $m$ at rest is acted upon by a force $F$ for a time $t$. Its Kinetic energy after an interval $t$ is

For a particle moving under the action of a variable force, kinetic energy-position graph is given, then

A shell of mass $200\, gm$ is ejected from a gun of  mass $4\, kg$ by an explosion that generates $1.05\, kJ$ of energy. The initial velocity of the shell is .............. $\mathrm{ms}^{-1}$

A block moving horizontally on a smooth surface with a speed of $40\, {m} / {s}$ splits into two parts with masses in the ratio of $1: 2$. If the smaller part moves at $60\, {m} / {s}$ in the same direction, then the fractional change in kinetic energy is :-