$A$ uniform cube of side $b$ and mass $M$ rests on a rough horizontal table. $A$ horizontal force $F$ is applied normal to one of the faces at a point at a height $3b/4$ above the base. What should be the coefficient of friction $\mu$ between the cube and the table so that it will tip about an edge before it starts slipping?

$A$ $300\ kg$ crate is dropped vertically onto a conveyor belt that is moving at $1.20\ m/s$. $A$ motor maintains the belt's constant speed. The belt initially slides under the crate,with a coefficient of friction of $0.400$. After a short time,the crate is moving at the speed of the belt. During the period in which the crate is being accelerated,find the work done by the motor which drives the belt :- ................. $J$

$A$ ball is dropped on the floor from a height of $20 \ m$. It rebounds to a height of $5 \ m$. The ball remains in contact with the floor for $1 \ s$. The average acceleration during contact is (acceleration due to gravity $g = 10 \ m/s^2$): (in $m/s^2$)

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.

$A$ force of $(2.6 \hat{i} + 1.6 \hat{j}) \text{ N}$ acts on a body of mass $2 \text{ kg}$. If the velocity of the body at time $t = 0$ is $(3.6 \hat{i} - 4.8 \hat{j}) \text{ ms}^{-1}$, the time at which the body will just have a velocity along the $x$-axis only is: (in $\text{ s}$)

$A$ balloon of total mass $M$ and a fixed size starts coming down with an acceleration $f$ $(f < g)$. The fraction of the total mass of the balloon which must be dropped from it so that it starts going up with an acceleration of $f$ (assuming negligible air resistance) is