$A$ particle of mass $M$ is moving in a horizontal circle of radius $R$ with uniform speed $v$. When the particle moves from one point to a diametrically opposite point,its

At a given instant of time,two particles have position vectors $4 \hat{i} + 4 \hat{j} + 57 \hat{k} \ m$ and $2 \hat{i} + 2 \hat{j} + 5 \hat{k} \ m$ respectively. If the velocity of the first particle is $0.4 \hat{i} \ ms^{-1}$,what is the velocity of the second particle in $ms^{-1}$ if they collide after $10 \ s$?

The diameter of a car wheel is $60 \ cm$. How many radians of angular displacement will the wheel have undergone while the car travels a distance of $1.2 \ km$?

$A$ ball is dropped from a height and falls due to gravity,while wind simultaneously imparts a uniform horizontal acceleration to it. Which one of the following figures best represents its path?

There are two points $P$ and $Q$ on a projectile path with velocities $v_P$ and $v_Q$ respectively,such that $v_P$ is perpendicular to $v_Q$. If $\alpha$ is the angle that $v_P$ makes with the horizontal at point $P$,find the correct option.

$A$ body moves along a circular path of radius $100 \,m$ and completes one revolution in $40 \,sec$. What is the total distance covered at the end of $2 \,min \,20 \,sec$ (in $\pi$)?