Two blocks,$4\, kg$ and $2\, kg$,are sliding down an inclined plane as shown in the figure. The acceleration of the $2\, kg$ block is ........ $m/s^2$.

In the figure shown,all surfaces are frictionless,and the mass of the block is $m = 1\, kg$. The block and wedge are held initially at rest. Now,the wedge is given a horizontal acceleration of $a = 10\, m/s^2$ by applying a force on the wedge,such that the block does not slip on the wedge. Calculate the work done by the normal force in the ground frame on the block in $\sqrt{3}$ seconds. (Assume $\tan \theta = a/g = 1$,so $\theta = 45^\circ$)

$A$ point particle of mass $m$ moves along the uniformly rough track $PQR$ as shown in the figure. The coefficient of friction between the particle and the rough track equals $\mu$. The particle is released from rest from the point $P$ and it comes to rest at a point $R$. The energies lost by the particle over the parts $PQ$ and $QR$ of the track are equal to each other,and no energy is lost when the particle changes direction from $PQ$ to $QR$. The values of the coefficient of friction $\mu$ and the distance $x (= QR)$ are,respectively,close to

When a bicycle is in motion,the force of friction exerted by the ground on the two wheels is such that it acts

For the given system,find the tension $T_2$ in the upper string.

$A$ block of mass $0.18 \ kg$ is attached to a spring of force-constant $2 \ N/m$. The coefficient of friction between the block and the floor is $0.1$. Initially,the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of $0.06 \ m$ and comes to rest for the first time. The initial velocity of the block in $m/s$ is $v = N/10$. Then $N$ is: