The velocity of a body at time $t = 0$ is $10\sqrt{2} \, m/s$ in the north-east direction and it is moving with an acceleration of $2 \, m/s^2$ directed towards the south. The magnitude and direction of the velocity of the body after $5 \, s$ will be

Read each statement below carefully and state,with reasons,if it is true or false:
$(a)$ The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre.
$(b)$ The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.
$(c)$ The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.

$A$ bomb is dropped from an aeroplane moving horizontally at a constant speed. When air resistance is taken into consideration,the bomb

Two cars of masses $m_{1}$ and $m_{2}$ are moving in circles of radii $r_{1}$ and $r_{2}$ respectively. Their speeds are such that they make complete circles in the same time $t$. The ratio of their centripetal force is

$A$ person sitting in an open car moving at a constant velocity throws a ball vertically up into the air. The ball falls:

$A$ ball is thrown from the ground at an angle $\theta$ with the horizontal and with an initial speed $u_0$. For the resulting projectile motion,the magnitude of the average velocity of the ball up to the point when it hits the ground for the first time is $V_1$. After hitting the ground,the ball rebounds at the same angle $\theta$ but with a reduced speed of $u_0 / \alpha$. Its motion continues for a long time as shown in the figure. If the magnitude of the average velocity of the ball for the entire duration of motion is $0.8 V_1$,the value of $\alpha$ is: