A gun applied a force $F$ on a bullet which is given by $$F=\left(100-0.5 \times 10^5 t\right) \mathrm{N}$$. The bullet emerges out with speed $$400 \mathrm{~m} / \mathrm{s}$$. Then find out the impulse exerted till force on the bullet becomes zero.

Assertion : A glass ball is dropped on concrete floor can easily get broken compared if it is dropped on wooden floor.

Reason : On concrete floor glass ball will take less time to come to rest.

A wooden wedge of mass $$M$$ and inclination angle $$(\alpha)$$ rest on a smooth floor. A block of mass $m$ is kept on wedge. A force $$F$$ is applied on the wedge as shown in the figure such that block remains stationary with respect to wedge. So, magnitude of force $$F$$ is

A piece of ice slides down a rough inclined plane at $$45^{\circ}$$ inclination in twice the time that it takes to slide down an identical but frictionless inclined plane. What is the coefficient of friction between ice and incline?

A body of mass 5 kg is suspended by a spring balance on an inclined plane as shown in figure.

So, force applied on spring balance is

In the figure, blocks A and B of masses 2m and m are connected with a string and system is hanged vertically with the help of a spring. Spring has negligible mass. Find out magnitude of acceleration of masses 2m and m just after the instant when the string is cut

In the figure, mass of a ball is $$\frac{9}{5}$$ times mass of the rod. Length of rod is $$1 \mathrm{~m}$$. The level of ball is same as rod level. Find out time taken by the ball to reach at upper end of rod.

Assertion Angle of repose is equal to angle of limiting friction.

Reason When a body is just at the point of motion, the force of friction of this stage is called as limiting friction.

With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is $$2 / 3$$ of the weight?

Four blocks of same mass connected by strings are pulled by a force $$F$$ on a smooth horizontal surface as shown in figure. The tension $$T_1, T_2$$ and $$T_3$$ will be

A body of mass $$5 \times 10^{-3} \mathrm{~kg}$$ is launched upon a rough inclined plane making an angle of $$30^{\circ}$$ with the horizontal. Obtain the coefficient of friction between the body and the plane if the time of ascent is half of the time of descent.