Two bodies of mass 1 ~kg and 3 ~kg have position vectors i+2 j+ k and -3 i-2 j+ k, respectively. The centre of mass of this system has a position…

A bullet of mass 10 g moving with 400 m/s penetrates a wall and comes to rest. The loss in kinetic energy is:

A body weighs 48 N on the surface of the earth. The gravitational force experienced by the body due to the earth at a height equal to one-third the radius of the earth from its surface is :

There are two inclined surface of equal length (L) and same angle of inclination $45^{\circ}$ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction $\left(\mu_k\right)$ between the object and the rough surface is close to :

In some appropriate units, time $(t)$ and position ( x ) relation of a moving particle is given by $t=x^2+x$. The acceleration of the particle is

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 $\mathrm{km} / \mathrm{h}$ in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.