$A$ body of mass $2 \,kg$ is moving with a constant acceleration of $(2 \hat{i}+3 \hat{j}-\hat{k}) \,ms^{-2}$. If the displacement made by the body is $(3 \hat{i}-\hat{j}+2 \hat{k}) \,m$, then the work done is: (in $\,J$)

$A$ particle of mass $M$ moving along the $X$-axis with speed $V_0$ collides with and sticks to another particle of mass $m$ moving along the $Y$-axis with speed $V_0$. What will be the velocity of the combined mass after the collision?

$A$ $2 \ kg$ block slides on a horizontal floor with a speed of $4 \ m/s$. It strikes an uncompressed spring and compresses it until the block is motionless. The kinetic friction force is $15 \ N$ and the spring constant is $10,000 \ N/m$. The spring compresses by ............. $cm$.

Fill in the blanks:
$(a)$ If the momentum of an object is doubled,its kinetic energy becomes ........
$(b)$ For a perfectly inelastic collision,the coefficient of restitution $e$ $=$ .....
$(c)$ An appliance with $1\,kW$ power consumes $1\,kWh$ of energy in ....... time.

State whether the following statements are true or false:
$(a)$ If the magnitude of force and length are increased by $4$ times,the magnitude of energy increases by $16$ times.
$(b)$ In an inelastic collision,both momentum and energy are conserved.
$(c)$ If work is done on a system by non-conservative forces,the potential energy increases.

$A$ block of mass $M = 1 \ kg$ is released from rest at the top of a smooth track of radius $R = 40 \ m$. The block slides along the track without toppling,and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point $Q$ (where the radius makes an angle of $30^{\circ}$ with the horizontal),as shown in the figure,is $150 \ J$. (Take the acceleration due to gravity,$g = 10 \ m s^{-2}$)
$1.$ The speed of the block when it reaches the point $Q$ is:
$(A) 5 \ m s^{-1}$ $(B) 10 \ m s^{-1}$ $(C) 10\sqrt{3} \ m s^{-1}$ $(D) 20 \ m s^{-1}$
$2.$ The magnitude of the normal reaction that acts on the block at the point $Q$ is:
$(A) 7.5 \ N$ $(B) 8.6 \ N$ $(C) 11.5 \ N$ $(D) 22.5 \ N$
Give the answers for question $1$ and $2$.