$A$ bullet of mass $m$ moving with velocity $v_1$ strikes a wooden block of mass $M$ suspended as shown in the figure and gets embedded in it. If the block rises to a height $h$,what is the initial velocity of the bullet?

$A$ force of $10 \ N$ acting at an angle on a particle produces a displacement of $(3 \hat{i} - 4 \hat{\jmath}) \ m$. Due to this force,if the kinetic energy of the particle is decreased by $25 \ J$,then the angle between the force and the displacement is:

Three objects $A, B$,and $C$ are placed on a frictionless horizontal surface. Their masses are $m, 2m$,and $m$ respectively. Object $A$ moves towards $B$ with a speed of $9 \ m/s$ and undergoes an elastic collision with it. Subsequently,$B$ undergoes a perfectly inelastic collision with $C$. All motion occurs along the same straight line. What will be the final speed of object $C$ in $m/s$?

$A$ truck pulls a mass of $1200 \ kg$ at a constant speed of $10 \ m/s$ on a level road. The tension in the coupling is $1000 \ N$. The power used on the mass will be ..... . When the truck moves on an incline of $1 \ m$ rise in $6 \ m$ length,the tension will be ..... .

If a lighter body (mass $M_1$ and velocity $V_1$) and a heavier body (mass $M_2$ and velocity $V_2$) have the same kinetic energy,then

$A$ block moving horizontally on a smooth surface with a speed of $40\, m/s$ splits into two parts with masses in the ratio of $1:2$. If the smaller part moves at $60\, m/s$ in the same direction,then the fractional change in kinetic energy is: