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 body of mass $2 \,kg$ is projected vertically upwards with a velocity of $2\,m\,{\sec ^{ – 1}}$. The K.E. of the body just before striking the ground is …………. $\mathrm{J}$

When kinetic energy of a body becomes $36$ times of its original value, the percentage increase in the momentum of the body will be :