$A$ body of mass $5 \,kg$ falls from a height of $30 \,m$. If all its mechanical energy is converted into heat,then the heat produced will be ........ $cal$.

$A$ particle of unit mass is moving along the $x$-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in column $I$ ($a$ and $U_0$ are constants). Match the potential energies in column $I$ to the corresponding statement$(s)$ in column $II$.

Column $I$	Column $II$
$(A) U_1(x) = \frac{U_0}{2} \left[1 - \left(\frac{x}{a}\right)^2\right]^2$	$(P)$ The force acting on the particle is zero at $x = a$.
$(B) U_2(x) = \frac{U_0}{2} \left(\frac{x}{a}\right)^2$	$(Q)$ The force acting on the particle is zero at $x = 0$.
$(C) U_3(x) = \frac{U_0}{2} \left(\frac{x}{a}\right)^2 \exp \left[-\left(\frac{x}{a}\right)^2\right]$	$(R)$ The force acting on the particle is zero at $x = -a$.
$(D) U_4(x) = \frac{U_0}{2} \left[\frac{x}{a} - \frac{1}{3}\left(\frac{x}{a}\right)^3\right]$	$(S)$ The particle experiences an attractive force towards $x = 0$ in the region $|x| < a$.
	$(T)$ The particle with total energy $\frac{U_0}{4}$ can oscillate about the point $x = -a$.

$A$ bullet of mass $m$ moving with velocity $v_1$ strikes a wooden block of mass $M$ suspended as shown in the figure and gets embedded in it. If the block rises to a height $h$,what is the initial velocity of the bullet?

$A$ block of mass $1.9\, kg$ is at rest at the edge of a table of height $1\, m$. $A$ bullet of mass $0.1\, kg$ collides with the block and sticks to it. If the velocity of the bullet is $20\, m/s$ in the horizontal direction just before the collision,then the kinetic energy just before the combined system strikes the floor is $....J$. (Take $g = 10\, m/s^2$. Assume there is no rotational motion and loss of energy after the collision is negligible.)

$A$ car of mass $1000 \ kg$ has a motor of efficiency $20 \%$. If burning of one litre of petrol supplies $6 \times 10^7 \ J$ of energy,the amount of petrol used in accelerating the car from rest to $43.2 \ km \ h^{-1}$ is (in $cc$)

$A$ ball of mass $0.2 \ kg$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2 \ m$ while applying the force and the ball goes up to $2 \ m$ height further,find the magnitude of the force $F$ in $N$. (Consider $g = 10 \ m/s^2$)