$A$ ball is dropped from a height of $5 \ m$ onto the floor of an elevator. The ball bounces off the floor. At the time of collision,the elevator is moving upwards with a velocity of $1 \ m/s$. What is the velocity of the ball immediately after the collision in $m/s$?

$A$ 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

$A$ constant force $F = m_2g/2$ is applied on the block of mass $m_1$ as shown in the figure. The string and the pulley are light and the surface of the table is smooth. The acceleration of $m_1$ is

In the figure,a block of weight $60 \, N$ is placed on a rough surface. The coefficient of friction between the block and the surface is $0.5$. Find the maximum weight $W$ such that the block does not slip on the surface.

In the figure,two blocks $M$ and $m$ are tied together with an inextensible and light string. The mass $M$ is placed on a rough horizontal surface with coefficient of friction $\mu$ and the mass $m$ is hanging vertically against a smooth vertical wall. The pulley is frictionless. Choose the correct statement$(s)$ related to the tension $T$ in the string.

$A$ block of mass $M$ is placed on a horizontal surface and it is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. If there is no friction between any two surfaces,then: