Water falls from a $40\,m$ high dam at the rate of $9 \times 10^{4}\,kg$ per hour. Fifty percent of the gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy, the number of $100\,W$ lamps that can be lit is (Take $g = 10\,m/s^2$)

$A$ particle of mass $m$ moving horizontally with velocity $v_0$ 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 $h$. Suppose the particle,when it reaches the horizontal surface again,has a velocity $v_1$ with respect to the ground,and the wedge has a velocity $v_2$. Choose the correct statement$(s)$.

From a building, two balls $A$ and $B$ are thrown such that $A$ is thrown upwards and $B$ is thrown downwards (both vertically) with the same speed. If $v_A$ and $v_B$ are their respective velocities on reaching the ground, then:

To maintain a speed of $80\,km/h$ by a bus of mass $500\,kg$ on a plane rough road for $4\,km$ distance,the work done by the engine of the bus will be $........\,kJ$. [The coefficient of friction between the tyre of the bus and the road is $0.04$].

$A$ 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 ................ $m/s^2$.

The friction coefficient between the horizontal surface and each of the blocks shown in the figure is $\mu = 0.2$. The collision between the blocks is perfectly elastic. What is the separation between the blocks when they come to rest? (in $cm$)