A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on the level ground, the magnitude of the change in momentum is

• $\sqrt{2} \mathrm{mv}$along -ve y-direction

• $\sqrt{2} \mathrm{mv}$ along +ve y-direction

• $2\sqrt{2} \mathrm{mv}$ along -ve y-direction

• $2\sqrt{2} \mathrm{mv}$ along +ve y-direction

The magnitude of vectors A, B and C are 3, 4 and 5 units respectively. If A + B =C, then the angle between A and B is

• $\frac{\mathrm{\pi }}{2}$

• cos^-1 0.6

• tan^-1 $\frac{7}{5}$

• $\frac{\mathrm{\pi }}{4}$

203.

A particle is projected upwards from the surface of the earth (of radius R) with a KE equal to half the minimum value needed for it to escape. To what height (h) does it rise above the surface of the earth

• R

• 2R

• $\frac{\mathrm{R}}{2}$

• (R)^1/2

The magnitude of a vector, on the addition of two vectors $6\stackrel{\wedge }{\mathrm{i}} + 7\stackrel{\wedge }{\mathrm{j}} \mathrm{and} 3\stackrel{\wedge }{\mathrm{i}} + 4\stackrel{\wedge }{\mathrm{j}}$ is

• $\sqrt{132}$

• $\sqrt{136}$

• $\sqrt{160}$

• $\sqrt{202}$

The acceleration experienced by a moving boat after its engine is cut off, is given by a = − kv³, where k is a constant. If v₀ is the magnitude of velocity at cut off, then the magnitude of the velocity at time t after the cut off is

• $\frac{{\mathrm{v}}_0}{2{{\mathrm{ktv}}_0}^2}$

• $\frac{{\mathrm{v}}_0}{1 + 2{{\mathrm{ktv}}_0}^2}$

• $\frac{{\mathrm{v}}_0}{\sqrt{1 - 2{{\mathrm{kv}}_0}^2}}$

• $\frac{{\mathrm{v}}_0}{\sqrt{1 + 2{{\mathrm{ktv}}_0}^2}}$

A passenger train is moving at 5 ms^-1 .An express train is travelling at 30 ms^-1, on the same track and rear side of the passenger train at some distance. The driver in express train applied brakes to avoid collision. If the retardation due to brakes is 4 ms^-2 , the time in which the accident is avoided after the application of brakes is

• 4.25 s

• 5.25 s

• 6.25 s

• 7.25 s

An aeroplane is flying horizontally with a velocity of 600 km/h and at a height of 1960 m. When it is vertically above a point A on the ground a bomb is released from it. The bomb strikes the ground at point B. The distance AB is

• 1200 m

• 0.33 km

• 333.3 km

• 3.33 km

A 10 kg object collides with stationary 5 kg object and after collision they stick together and move forward with velocity 4 ms^-1. What is the velocity with which the 10 kg object hit the second one ?

• 4 ms^-1

• 6 ms^-1

• 10 ms^-1

• 12 ms^-1

A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during the 5th second to that covered in 5 s is

• $\frac{9}{25}$

• $\frac{3}{5}$

• $\frac{25}{5}$

• $\frac{1}{25}$

An object is projected at an angle of 45° with the horizontal. The horizontal range and maximum height reached will be in the ratio 

• 1 : 2

• 2 : 1

• 1 : 4

• 4 : 1