Consider a point $P$ on the circumference of a disc rolling along a horizontal surface. If $R$ is the radius of the disc, the distance through which $P$ moves in one full rotation of the disc is
$2\pi R$
$4\pi R$
$8R$
$\pi R$
A ball is rolled off along the edge of a horizontal table with velocity $4 m/s$. It hits the ground after time $0.4 \,\,s$. Which of the following are correct?
A particle starts from origin at $t=0$ with a velocity $5.0 \hat{ i }\; m / s$ and moves in $x-y$ plane under action of a force which produces a constant acceleration of $(3.0 \hat{ i }+2.0 \hat{ j })\; m / s ^{2} .$
$(a)$ What is the $y$ -coordinate of the particle at the instant its $x$ -coordinate is $84 \;m$ ?
$(b)$ What is the speed of the particle at this time?
The trajectory of a projectile in a vertical plane is $y =\alpha x -\beta x ^{2},$ where $\alpha$ and $\beta$ are constants and $x \& y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained $H$ are respectively given by :-
The acceleration of a body in a non-uniform circular motion is $5\, ms^{-2}$. Which one of the following is correct?