An object of mass $M$ is placed on a rough horizontal surface (coefficient of friction $\mu$). $A$ person tries to pull the object by applying a horizontal force,but the object does not move. The force $F$ exerted by the surface on the object is:

At the moment $t=0$, a time-dependent force $F=at$ (where $a$ is a constant equal to $1 \,Ns^{-1}$) is applied to a body of mass $1 \,kg$ resting on a smooth horizontal plane as shown in the figure. If the direction of this force makes an angle $45^{\circ}$ with the horizontal, then the velocity of the body at the moment it leaves the plane is (acceleration due to gravity $=10 \,ms^{-2}$)

An electric lift with a maximum load of $2000\,kg$ (lift + passengers) is moving up with a constant speed of $1.5\,m/s$. The frictional force opposing the motion is $3000\,N$. The minimum power delivered by the motor to the lift in watts is: $(g=10\,m/s^2)$

On a pulley of mass $M$ hangs a rope with two masses $m_{1}$ and $m_{2}$ $(m_{1} > m_{2})$ tied at the ends as shown in the figure. The pulley rotates without any friction,whereas the friction between the rope and the pulley is large enough to prevent any slipping. Which of the following plots best represents the difference between the tensions in the rope on the two sides of the pulley as a function of the mass of the pulley?

When the bomb $Q$ explodes,the trolley of mass $200 \, kg$ travels a distance of $36 \, m$ before coming to rest. What distance will the trolley of mass $300 \, kg$ travel before coming to rest (in $, m$)?

$A$ 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 $\text{ s}$)