Two particles which are initially at rest,move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant,then the speed of the centre of mass of the system will be

When $100 \, V$ $DC$ is applied across a solenoid,a current of $1 \, A$ flows in it. When $100 \, V$ $AC$ is applied across the same coil,the current drops to $0.5 \, A$. If the frequency of the $AC$ source is $50 \, Hz$,the impedance and inductance of the solenoid are:

$A$ light string fixed at one end to a clamp on the ground passes over a fixed pulley and hangs on the other side. It makes an angle of $30^{\circ}$ with the ground. $A$ monkey of mass $5 \, kg$ climbs up the rope. The clamp can tolerate a vertical force of $40 \, N$ only. The maximum acceleration in the upward direction with which the monkey can climb safely is ............ $m/s^2$ (neglect friction and take $g = 10 \, m/s^2$).

Which artificial sweetener contains chlorine?

Select the wrong statement.

Which amino acids are present in histones?