Consider a frictionless ramp on which a smooth object is made to slide down from an initial height $h$. The distance $d$ necessary to stop the object on a flat track (of coefficient of friction $\mu$), kept at the ramp end, is:

$A$ train of mass $3 \times 10^6 \ kg$ is accelerated by an engine such that its velocity increases from $5 \ m/s$ to $25 \ m/s$ in $5 \ minutes$. The power of the engine is ........ $MW$.

$A$ ball of mass $0.2 \ kg$ rests on a vertical post of height $5 \ m$. $A$ bullet of mass $0.01 \ kg$,traveling with a velocity $V \ m/s$ in a horizontal direction,hits the centre of the ball. After the collision,the ball and bullet travel independently. The ball hits the ground at a distance of $20 \ m$ and the bullet at a distance of $100 \ m$ from the foot of the post. The initial velocity $V$ of the bullet is

$A$ 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 $4 \ kg$ is moving with a momentum of $8 \ kg \ m/s$. $A$ force of $0.2 \ N$ acts on it in the direction of motion for $10 \ s$. The increase in kinetic energy in joules is:

The potential energy in joules of a particle of mass $1\, kg$ moving in a plane is given by $U = 3x + 4y$,where the position coordinates $x$ and $y$ are measured in metres. If the particle is initially at rest at $(6, 4)$,then: