Laws of Motion ...

A stone, tied at the end of a string $$80$$ cm long, is whirled in a horizontal circle with a constant speed. If the stone makes $$14$$ revolutions in $$25$$ sec, what is the magnitude of acceleration of the stone.

A bullet of mass $$50\ g$$ travelling at $$500\ m/s$$ penetrates $$100\ cm$$ into a wooden block. Find the average force exerted on the block.

A field gun of mass 150 $$kg$$ fires a shell of mass 1 kg with velocity of 150 m/s. Calculate the velocity of the recoil of the gun.

A ball of weight $$0.1$$ kg coming with a speed $$30$$ m/s strikes a bat and returns in opposite direction with speed of $$40$$ m/s, then impulse is 

Velocity of a particle of mass $$2\ kg$$ varies with time $$t$$ according to the equation $$\vec {v} = (2t\hat {i} + 4\hat {j}) m/s$$. Here $$t$$ is in seconds. Find the impulse imparted to the particle in the time interval from $$t = 0$$ to $$t = 2s$$.

Two balls of same mass are dropped from the same height h , on to the floor . the first ball bounces to a height h/4, after the collection & the second ball to a height h/16. the impulse applied by the first & second ball on the floor are $${I_1}$$  and $${I_2}$$ respectively . then

Two particles A and B equal masses are respectively tied to the centre and one end of a string, whose other end 0 is fixed. Both the particles always revolve in concentric circles of centre O. The ratio of tensions in both the parts of the string will be

A stone of mass $$1\ kg$$ is tied to a string $$4\ m$$ long and is rotated at constant speed of $$40\ ms^{-1}$$ in a vertical circle. The ration of the tension at the top and the bottom is

Circular flexible current loop of radius R carrying current I is placed in an inward magnetic field B. If we spin the loop with angular speed $$/omega $$, then tension in string

A 40 N block is supported by two ropes. One rope is horizontal and the other makes an angle of $${30^ \circ }$$ with the ceiling. The tension in the rope attached to the ceiling is approximately: