A body is projected with a speed u m/s at an angle β with the horizontal. The kinetic energy at the highest point is $\frac{3}{4}$th of the initial kinetic energy. The value of β is

• 30°

• 45°

• 60°

• 120°

A ball is projected horizontally with a velocity of 5 m/s from the top of a building 19.6 m high. How long will the ball take to hit the ground ?

• $\sqrt{2} \mathrm{s}$

• 2 s

• $\sqrt{3} \mathrm{s}$

• 3 s

A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first three seconds of its motion. The stone remains in the air for

• 6 s

• 5 s

• 7 s

• 4 s

Two blocks of 2 kg and 1 kg are in contact on a frictionless table. If a force of 3 N is applied on 2 kg block, then the force of contact between the two blocks will be

• zero

• 1 N

• 2 N

• 3 N

If momentum is increased by 20%, then kinetic energy increases by

• 48 %

• 44 %

• 40 %

• 36 %

A boy of mass 40 kg is climbing a vertical pole at a constant speed. If the coefficient of friction between his palms and the pole is 0.8 and g = 10 m/s², the horizontal force that he is applying on the pole is

• 300 N

• 400 N

• 500 N

• 600 N

The value of λ for which the two vectors $\overrightarrow{\mathrm{a}} = 5 \hat{\mathrm{i}} + \mathrm{\lambda } \hat{\mathrm{j}} + \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{b}} = \hat{\mathrm{i}} - 2 \hat{\mathrm{j}} + \hat{\mathrm{k}}$ are perpendicular to each other is

• 2

• - 2

• 3

• - 3

If $\overrightarrow{\mathrm{a}} + \overrightarrow{\mathrm{b}} = \overrightarrow{\mathrm{c}}$ and a + b = c, the the angle included between $\overrightarrow{\mathrm{a}} \mathrm{and} \overrightarrow{\mathrm{b}}$ is

• 90°

• 180°

• 120°

• zero

The height vertically above the earth's surface at which the acceleration due to gravity becomes 1% of its value at the surface is (R is the radius of the earth)

• 8 R

• 9 R

• 10 R

• 20 R

The change in the gravitational potential energy when a body of mass m is raised to a height nR above the surface of the Earth is (Here R is the radius of the earth)

• $\left(\frac{\mathrm{n}}{\mathrm{n} + 1}\right) \mathrm{mgR}$

• $\left(\frac{\mathrm{n}}{\mathrm{n} - 1}\right) \mathrm{mgR}$

• nmgR

• $\frac{\mathrm{mgR}}{\mathrm{n}}$