A rockel weighs $15000 \mathrm{kg}$ when it is on the launching pad on the surface of the earth. It is fired vertically upward and after all the fuel is burnt out, it weighs $5000 \mathrm{kg}$. The ejection of the fuel gas is at a constant rate of $5 {\mathrm{kgs}}^{-1}$ with a constant velocity of $1700{ \mathrm{ms}}^{-1}$ relative to the rocket.

Calculate the thrust of the rocket (Neglect gravity and air resistance.)

A rockel weighs $15000 \mathrm{kg}$ when it is on the launching pad on the surface of the earth. It is fired vertically upward and after all the fuel is burnt out, it weighs $5000 \mathrm{kg}$. The ejection of the fuel gas is at a constant rate of $5 {\mathrm{kgs}}^{-1}$ with a constant velocity of $1700{ \mathrm{ms}}^{-1}$ relative to the rocket.

Calculate the final speed of the rocket after complete burn out of the fuel. (Neglect gravity and air resistance.)

Two cubes of masses $m_1$ and $m_2$ lie on two frictionless slopes of block $A$ which rests on a horizontal table. The cubes are connected by a string which passes over a pulley. (See Fig.) To what horizontal acceleration should the whole system (i.e., the block and cubes) be subjected so that the cubes do not slide down the plane? What is the tension in the sring in this situation?

Two blocks of mass $2.9 \mathrm{kg}$ and $1.9 \mathrm{kg}$ are suspended from a rigid support $S$ by two inextensible wires each of length 1 metre, see Fig. The upper wire has negligible mass and the lower wire has a uniform mass of $0.2 \mathrm{kg}/\mathrm{m}$. The whole system of blocks, wires and support have an upward acceleration of $0.2 \mathrm{m}/{\mathrm{s}}^2$. Acceleration due to gravity is $9.8 \mathrm{m}/{\mathrm{s}}^2$.

Find the tension at the mid-point of lower wire,

Two blocks of mass $2.9 \mathrm{kg}$ and $1.9 \mathrm{kg}$ are suspended from a rigid support $S$ by two inextensible wires each of length 1 metre, see  . The upper wire has negligible mass and the lower wire has a uniform mass of $0.2 \mathrm{kg}/\mathrm{m}$. The whole system of blocks, wires and support have an upward acceleration of $0.2 \mathrm{m}/{\mathrm{s}}^2$. Acceleration due to gravity is $9.8 \mathrm{m}/{\mathrm{s}}^2$.

Find the tension at the mid-point of upper wire

A body of mass $m$ moving with a velocity $v$ in the $X$ direction collides with another body of mass $M$ moving in the $Y$ -direction with a velocity $V$. They coalesce into one body during collision.

Calculate the direction and magnitude of the momentum of the final body,

A body of mass $m$ moving with a velocity $v$ in the $X$ direction collides with another body of mass $M$ moving in the $Y$ -direction with a velocity $V$. They coalesce into one body during collision.

Calculate the fraction of initial kinetic energy transformed into heat during collision in terms of the two masses.