$A$ lift of mass $2000 \ kg$ starts from rest in the basement and moves to the fourth floor,which is at a height of $25 \ m$. As it passes the fourth floor,its speed is $3 \ ms^{-1}$. There is a constant frictional force of $500 \ N$ acting on it. Calculate the work done by the lift's motor in $kJ$.

$A$ point mass of $1 \, kg$ collides elastically with a stationary point mass of $5 \, kg$. After their collision, the $1 \, kg$ mass reverses its direction and moves with a speed of $2 \, m/s$. Which of the following statement(s) is (are) correct for the system of these two masses?
$(A)$ Total momentum of the system is $3 \, kg \cdot m/s$
$(B)$ Momentum of $5 \, kg$ mass after collision is $4 \, kg \cdot m/s$
$(C)$ Kinetic energy of the centre of mass is $0.75 \, J$
$(D)$ Total kinetic energy of the system is $4 \, J$

On complete combustion,a litre of petrol releases heat equivalent to $3 \times 10^7 \, J$. In a test drive,a car weighing $1200 \, kg$ (including the driver) travels $15 \, km$ per litre while moving at a uniform speed on a straight track. Assuming that the friction offered by the road surface and air is uniform,calculate the force of friction acting on the car during the test drive,given that the efficiency of the car engine is $0.5$. (in $, N$)

$A$ particle of mass $m$ moving horizontally with $v_0$ strikes a smooth wedge of mass $M$,as shown in the figure. After the collision,the ball starts moving up the inclined face of the wedge and rises to a height $h$. Identify the correct statement$(s)$ related to the situation when the particle starts moving downward.

$A$ block of mass $m = 0.1\,kg$ is connected to a spring of unknown spring constant $k.$ It is compressed to a distance $x$ from its equilibrium position and released from rest. After approaching half the distance $(\frac{x}{2})$ from the equilibrium position,it hits another block and comes to rest momentarily,while the other block moves with a velocity $3\,m/s.$ The total initial energy of the spring is ................ $J$.

$A$ person trying to lose weight by burning fat lifts a mass of $10 \ kg$ up to a height of $1 \ m$, $1000$ times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies $3.8 \times 10^7 \ J$ of energy per $kg$, which is converted to mechanical energy with a $20\%$ efficiency rate. Take $g = 9.8 \ m/s^2$.