$A$ body of mass $1\,kg$ is thrown upwards with a velocity $20\,m/s$. It momentarily comes to rest after attaining a height of $18\,m$. How much energy is lost due to air friction? (Given $g = 10\,m/s^2$)

Two balls,having linear momenta $\vec{p}_1 = p \hat{i}$ and $\vec{p}_2 = -p \hat{i}$,undergo a collision in free space. There is no external force acting on the balls. Let $\vec{p}_1^{\prime}$ and $\vec{p}_2^{\prime}$ be their final momenta. Which of the following option$(s)$ is (are) $NOT ALLOWED$ for any non-zero value of $p, a_1, a_2, b_1, b_2, c_1$ and $c_2$?
$(A)$ $\vec{p}_1^{\prime} = a_1 \hat{i} + b_1 \hat{j} + c_1 \hat{k}$,$\vec{p}_2^{\prime} = a_2 \hat{i} + b_2 \hat{j}$
$(B)$ $\vec{p}_1^{\prime} = c_1 \hat{k}$,$\vec{p}_2^{\prime} = c_2 \hat{k}$
$(C)$ $\vec{p}_1^{\prime} = a_1 \hat{i} + b_1 \hat{j} + c_1 \hat{k}$,$\vec{p}_2^{\prime} = a_2 \hat{i} + b_2 \hat{j} - c_1 \hat{k}$
$(D)$ $\vec{p}_1^{\prime} = a_1 \hat{i} + b_1 \hat{j}$,$\vec{p}_2^{\prime} = a_2 \hat{i} + b_1 \hat{j}$

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ until the mass comes to rest,as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block
According to observer $B$,the potential energy of the spring increases:

Water falls from a height of $60 \, m$ at the rate of $15 \, kg/s$ to operate a turbine. The losses due to frictional force are $10 \%$ of the input energy. How much power is generated by the turbine? $(g=10 \, m/s^2)$ (In $kW$)

$A$ ball of mass $2 \,kg$ is thrown from a tall building with velocity $v = (20 \,m/s) \hat{i} + (24 \,m/s) \hat{j}$ at time $t = 0 \,s$. The change in the potential energy of the ball after $t = 8 \,s$ is (The ball is assumed to be in air during its motion between $0 \,s$ and $8 \,s$, $\hat{i}$ is along the horizontal and $\hat{j}$ is along the vertical direction. Take $g = 10 \,m/s^2$). (in $\,kJ$)

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