$A$ simple pendulum of length $1 \ m$ has a bob of mass $1 \ kg$. $A$ bullet of mass $10^{-2} \ kg$ is fired into the bob with a speed of $2 \times 10^2 \ m/s$. The bullet gets embedded in the bob. Find the height $h$ to which the bob rises before it swings back. (in $m$)

$A$ wooden block of mass $M$ is suspended by a cord and is at rest. $A$ bullet of mass $m$,moving with a velocity $v$,passes through the block and emerges with a velocity $v/2$ in the same direction. If the block rises to a height $H$,calculate the value of $H$.

The mass of a person is $60 \, kg$. If he gains $10^5 \, \text{calories}$ of heat energy from food and the efficiency of his body is $28 \%$,then up to what height can he climb? (approximately) ($g = 9.8 \, m/s^2$,$J = 4.2 \, J/\text{cal}$)

$A$ mass of $2.9 \ kg$ is suspended from a string of length $50 \ cm$ and is at rest. Another body of mass $100 \ g$,which is moving horizontally with a velocity of $150 \ m/s$,strikes and sticks to it. Subsequently,when the string makes an angle of $60^{\circ}$ with the vertical,the tension in the string is $(g = 10 \ m/s^2)$. (in $N$)

$A$ body of mass $500 \ g$ is falling from rest from a height of $3.2 \ m$ from the ground. If the body reaches the ground with a velocity of $6 \ ms^{-1}$, then the energy lost by the body due to air resistance is (Acceleration due to gravity $= 10 \ ms^{-2}$) (in $J$)

$A$ truck of mass $M$ and a car of mass $\frac{M}{10}$ moving with the same momentum are brought to a halt by the application of the same braking force. The ratio of the distances travelled by the truck and the car before they come to a stop is