$A$ body is sliding down an inclined plane having a coefficient of friction $0.5$. If the normal reaction is twice that of the resultant downward force along the incline,the angle between the inclined plane and the horizontal is ....... $^o$

$A$ bob of mass $m$ is attached to a string of length $\ell$ whose other end is tied to a light vertical rod as shown in the figure. The bob is swinging in a horizontal plane with a constant angular speed $\omega$. The vertical rod is supported on a block of mass $M$ which is placed on a rough surface. What is the minimum friction coefficient between the ground and the block for which the block does not slip?

$A$ block of mass $2 \, kg$ is placed on a rough inclined plane as shown in the figure $(\mu = 0.2)$ so that it just touches the spring. The block is allowed to move downwards. The spring will be compressed to a maximum of .............. $cm$.

$A$ block of mass $10 \ kg$, initially at rest, makes a downward motion on a $45^{\circ}$ inclined plane. The distance travelled by the block after $2 \ s$ is (Assume the coefficient of kinetic friction to be $0.3$ and $g=10 \ m/s^2$)

$A$ block of mass $m$ is placed on a wedge of angle $\theta$. The wedge is moving with a constant velocity $v$ on a horizontal surface. If the block does not slide on the wedge,find the work done by the friction force on the block in time $t$.

$A$ block of weight $1 \,N$ rests on an inclined plane of inclination $\theta$ with the horizontal. The coefficient of friction is $\mu$. The minimum force that has to be applied parallel to the inclined plane to make the body just move up the plane is