The range of a projectile of mass $1\, kg$ is $80\, m$ while it attains a maximum height of $20\, m$. Its change in momentum during the complete motion is ............ $N-s$.

Two balls are projected from the same point simultaneously. The first ball is projected vertically upwards with velocity $u_1$ and the second ball at an angle of projection $60^{\circ}$ to the ground level with velocity $u_2$. Both the balls reach the ground simultaneously. The ratio of their velocities $u_1 : u_2$ is

The position vector of a particle $\vec{R}$ as a function of time is given by $\vec{R} = 4\sin(2\pi t)\hat{i} + 4\cos(2\pi t)\hat{j}$,where $R$ is in meters,$t$ is in seconds,and $\hat{i}$ and $\hat{j}$ denote unit vectors along $x$- and $y$-directions,respectively. Which one of the following statements is wrong for the motion of the particle?

Two balls are thrown with the same velocity,one vertically upward and the other at an angle of $60^\circ$ with the vertical. What is the ratio of their potential energies at their respective maximum heights?

If a body moving in a circular path maintains a constant speed of $10\,ms^{-1},$ then which of the following correctly describes the relation between acceleration and radius?

Will the linear velocity of a particle rotating with a constant angular speed about a non-fixed axis be constant? Why?