$A$ body is projected up along a rough inclined plane of inclination $45^{\circ}$. The coefficient of friction is $0.5$. Then the retardation of the block is

$A$ block of mass $1 \,kg$ slides down on a rough inclined plane of inclination $60^\circ$ starting from its top. If the coefficient of kinetic friction is $0.5$ and the length of the plane is $1 \,m$,then the work done against friction is ........ $J$.

Two touching blocks $1$ and $2$ are placed on an inclined plane forming an angle $60^{\circ}$ with the horizontal. The masses are $m_1$ and $m_2$ and the coefficients of friction between the inclined plane and the two blocks are $1.5 \mu$ and $1.0 \mu$, respectively. The force of reaction between the blocks during the motion is ($g=$ acceleration due to gravity).

$A$ block of mass $5 \, kg$ is placed on a rough inclined plane with an angle of $30^\circ$. If the block moves down with a constant velocity,what is the coefficient of friction? (Take $g = 10 \, m/s^2$)

The upper half of an inclined plane of inclination $\theta$ is smooth,while the lower half is rough. If a block released from the top comes to rest at the bottom,what is the coefficient of friction between the block and the rough surface?

Starting from rest,the time taken by a body sliding down on a rough inclined plane at $45^{\circ}$ with the horizontal is twice the time taken to travel on a smooth plane of the same inclination and same distance. Then the coefficient of kinetic friction is