Impulse and Conservation of Momentum

A 600 kg rocket is set for a vertical firing. If the exhaust speed is 1000 $m{s}^{-}{}^1,$ the mass of the gas ejected per second to supply the thrust needed to overcome the weight of rocket is :

A $5000 \mathrm{kg}$ rocket is set for a vertical firing. The exhaust speed is $800 \mathrm{m} {\mathrm{s}}^{-1}$. To give an initial upward acceleration of $30 m {\mathrm{s}}^{-2}$, the amount of gas ejected (in $\mathrm{kg} {\mathrm{s}}^{-1}$) to supply the needed thrust will be (Take $g=10 m {\mathrm{s}}^{-2}$)

Negative acceleration occurs in the opposite direction of:

A particle moves a distance $\mathrm{x}$ in time $\mathrm{t}$ according to equation $\mathrm{x}={\left(\mathrm{t}+5\right)}^{-1}$. The acceleration of particle is proportional to

The velocity of a body, moving in a plane, changes from $3\hat{\mathrm{i}}$ to $3\hat{\mathrm{i}}+7\hat{\mathrm{j}}$ in $10\sec$. What is the acceleration of the body?

A weight of $500\mathrm{N}$ is help on a smooth plane, inclined at ${30}^{\mathrm{o}}$ to the horizontal by a force $\mathrm{P}$ acting ${30}^{\mathrm{o}}$ above the plane as shown by the figure. The reaction of the plane on the weight will be:

The co-efficient of friction $\mathrm{\mu }$ and the angle of friction $\mathrm{\theta }$ are related as

A body is resting on a plane inclined at angle ${30}^{\mathrm{o}}$, to horizontal. What force would be required to slide it down, if the co-efficient of friction between body and plane is $0.3$?

A box weight $1000\mathrm{N}$ is placed on the ground. The co-efficient of friction between the box and th ground is $0.5$. When the box is pulled by a $100\mathrm{N}$ horizontal force, the frinctional force developed between the box and ground at imepending motion is 

A block of mass $5\mathrm{kg}$ slides down from rest along a frictionless inclined plane that makes an angle of ${30}^{\mathrm{o}}$ with horizontal. What will be the speed of the  block after it covers a distance of $3.6\mathrm{m}$ along the plane?$\left[\mathrm{g}=10 \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right.\right]$

A ball of $1 \mathrm{kg}$ drops vertically on the floor with a speed of $25 \mathrm{m}/\mathrm{s}$. It rebounds with a velocity of $10{ \mathrm{ms}}^{-1}$.

What impulse acts on the ball during contact?

A nucleus disintegrates into two nuclear parts which have their velocities in the ratio $2:1$. The ratio of their nuclear sizes will be

The difference between the working of a jet and a rocket is

A man throws a ball straight up. The ball has a momentum in the vertically upward direction.The principle of conservation of momentum demands that the earth has

A jet engine works on the principle of

Two balls having linear momenta ${\overrightarrow{p}}_1=p\hat{\mathrm{i}}$ and ${\overrightarrow{p}}_2=-p\hat{\mathrm{i}}$, undergo a collision in free space. There is no external force acting on the balls. Let ${\overrightarrow{p}}_1^{\text{'}}$ and ${\overrightarrow{p}}_2^{\text{'}}$ be their final momenta. The following option (s) is (are) not allowed for any non-zero value of $p, a_1, a_2, b_1, b_2, c_1$ and $c_2$.

A man of mass $50 \mathrm{kg}$ is standing at one end of a boat of length $25 \mathrm{m}$ and mass $200 \mathrm{kg}$. He starts running and when he reaches the other end, he has a velocity $2{ \mathrm{ms}}^{-1}$ with respect to the boat. The final velocity of the boat is (in ${\mathrm{ms}}^{-1}$)

The rate of mass of the gas emitted from rear of a rocket is initially $0.1 {\mathrm{kgs}}^{-1}$. If the speed of the gas relative to the rocket is $50{ \mathrm{ms}}^{-1}$ and mass of the rocket is $2 \mathrm{kg}$, then the acceleration of the rocket (in ${\mathrm{ms}}^{-2}$) is 

A shell of mass $10 \mathrm{kg}$ is moving with a velocity of $10{ \mathrm{m} \mathrm{s}}^{-1}$ when it blasts and forms two parts of mass $9 \mathrm{kg}$ and $1 \mathrm{kg}$ respectively. If the 1st mass is stationary, the velocity of the $2\mathrm{nd}$ is