Morning breakfast provides $5000 \,cal$ of energy to a $60 \,kg$ person. The efficiency of the person is $30 \%$. The height up to which the person can climb using the energy obtained from the breakfast is ......... $m$.

$A$ ball is dropped from a height of $5\,m$ onto a sandy floor and penetrates the sand up to $1\,m$ before coming to rest. The retardation of the ball in sand (assuming it to be uniform) will be ................ $m/s^2$.

$A$ water pump is driven by a petrol engine that pumps water from a depth of $30 \ m$ at a rate of $0.5 \ m^3/min$. If the efficiency of the pump is $70\%$, what is the power generated by the engine in $W$?

$A$ $0.5 \, kg$ block moving at a speed of $12 \, ms^{-1}$ compresses a spring through a distance of $30 \, cm$ when its speed is halved. The spring constant of the spring in $N m^{-1}$ is:

$A$ slide with a frictionless curved surface,which becomes horizontal at its lower end,is fixed on the terrace of a building of height $3h$ from the ground,as shown in the figure. $A$ spherical ball of mass $m$ is released on the slide from rest at a height $h$ from the top of the terrace. The ball leaves the slide with a velocity $\vec{u}_0 = u_0 \hat{x}$ and falls on the ground at a distance $d$ from the building,making an angle $\theta$ with the horizontal. It bounces off with a velocity $\vec{v}$ and reaches a maximum height $h_1$. The acceleration due to gravity is $g$ and the coefficient of restitution of the ground is $e = 1 / \sqrt{3}$. Which of the following statement$(s)$ is(are) correct?
$(A)$ $\vec{u}_0 = \sqrt{2gh} \hat{x}$
$(B)$ $\vec{v} = \sqrt{2gh} \hat{x} + \sqrt{2gh} \hat{z}$
$(C)$ $\theta = 60^{\circ}$
$(D)$ $d / h_1 = 2\sqrt{3}$

Name the instrument used to measure the coefficient of restitution of a material and explain why frictional force is a non-conservative force.