G L Mittal and TARUN MITTAL Solutions for Chapter: Force : Newton's Laws of Motion, Exercise 2: NUMERICALS

A uniform shell at rest explodes into three equal parts. Two of the parts fly off perpendicular to each other with velocities $9 \mathrm{m}/\mathrm{s}$ and $12 \mathrm{m}/\mathrm{s}$. Find the velocity of the third part.

A body of mass $1 \mathrm{kg}$ initially at rest, explodes and breaks into three fragments of masses in the ratio $1:1:3$. The two fragments of equal masses fly off perpendicular to each other with a speed of $30 \mathrm{m}/\mathrm{s}$ each. What is the velocity of the heavier fragment?

 Determine the magnitude and direction of the combined momentum of the moving spheres shown in the figure by drawing a vector diagram. $m_1=2 \mathrm{kg}$, $m_3=3 \mathrm{kg}$, $v_1=6 \mathrm{m}/\mathrm{s}$, $v_2=4\mathrm{m}/\mathrm{s}$. 

The velocities of two bodies(masses $5 \mathrm{kg}$ and $10 \mathrm{kg}$) in the $+x$ and the $+y$ directions are $4 \mathrm{m}/\mathrm{s}$ and $2 \mathrm{m}/\mathrm{s}$ respectively. They collide and stick together. What is the final velocity?

A metallic block of mass $2 \mathrm{kg}$ is resting on a frictionless plane. It is struck by a jet releasing water at a rate of $1 \mathrm{kg}/\mathrm{s}$ and at a speed of $5 {\mathrm{ms}}^{-1}$. Find the initial acceleration of the block.

The mass of a rocket is $1.3\times {10}^4 \mathrm{kg}$. Its engine exerts on it an initial thrust of $2.6\times {10}^5 \mathrm{N}$ in the upward direction. Calculate the initial acceleration attained by the rocket$\left(g=9.8 \mathrm{m}/{\mathrm{s}}^2\right)$.

In a rocket fuel is burnt at the rate of $100 \mathrm{kg}/\mathrm{s}$ and burnt gases rush at a speed of $5\times {10}^4 \mathrm{m}/\mathrm{s}$. Find the thrust of the rocket ignoring gravity.

In a rocket, the mass of the fuel is $90\%$ of the total mass. The exhaust gases are ejected at a speed of $2 {\mathrm{kms}}^{-1}$. Find the maximum speed attained by the rocket. Neglect gravity and air resistance and take the initial speed of the rocket to be zero. Given : ${\log }_{e}10=2.3$