From the $v - t$ graph shown, the ratio of distance to displacement in 25 s of motion is: [Figure] (1) 1 (2) $\frac{1}{2}$ (3) $\frac{5}{3}$ (4) $\frac{3}{5}$
A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the centre. If the angular velocity of the table is halved, it will just slip when placed at a distance of $\_\_\_\_$ from the centre: (1) 8 cm (2) 4 cm (3) 1 cm (4) 2 cm
An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of $250 \mathrm{~m}\mathrm{~s}^{-1}$ to keep it in position. The number of bullets fired per second by the machine gun is: (1) 50 (2) 25 (3) 100 (4) 5
The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement ($x$) starting from mean position to extreme position ($A$) is given by (1)[Figure] (2)[Figure] (3)[Figure] (4)[Figure]
A projectile fired at $30^\circ$ to the ground is observed to be at same height at time 3 s and 5 s after projection, during its flight. The speed of projection of the projectile is $\_\_\_\_$ $\mathrm{m}\mathrm{~s}^{-1}$. (Given $g = 10$ m s$^{-2}$)
A force $\vec{F} = (2 + 3x)\hat{i}$ acts on a particle in the $x$ direction where $F$ is in Newton and $x$ is in meter. The work done by this force during a displacement from $x = 0$ to $x = 4$ m is $\_\_\_\_$ J.