A stone of mass 2 kg is tied to a string of length 0.5 m. If the breaking tension of the string is 900 N, then the maximum angular velocity, the stone can have in uniform circular motion is

• 30 rad s^-1

• 20 rad s^-1

• 10 rad s^-1

• 25 rad s^-1

The resultant of two vectors $\overrightarrow{\mathrm{P}}$ and $\overrightarrow{\mathrm{Q}}$ is $\overrightarrow{\mathrm{R}}$. If the magnitude of $\overrightarrow{\mathrm{Q}}$ is doubled, the new resultant becomes perpendicular to $\overrightarrow{\mathrm{P}}$. Then the magnitude of $\overrightarrow{\mathrm{R}}$ is 

• P + Q

• Q

• P

• $\frac{\mathrm{P} + \mathrm{Q}}{2}$

A motor car is moving with a speed of 20 ms^-1 on a circular track of radius 100 m. If its speed is increasing at the, rate of 3 ms^-1, its resultant acceleration is

• 3 ms^-2

• 5 ms^-2

• 2.5 ms^-2

• 3.5 ms^-2

An object is dropped from rest. Its v-t graph is

Two particles A and B are projected with same speed so that the ratio of their maximum heights reached is 3 : 1. If the speed of A is doubled without altering other parameters, the ratio of the horizontal ranges attained by A and B is

• 1 : 1

• 2 : 1

• 4 : 1

• 3 : 2

An object of mass 5 kg is attached to the hook of a spring balance and the balance is suspended vertically from the roof of a lift. The reading on the spring balance when the lift is going up with an acceleration of 0.25 ms^-2 is (g = 10 ms^-2)

• 51.25 N

• 48.75 N

• 52.75 N

• 47.25 N

67.

A ball is projected from the ground at a speed of 10 ms^-1 making an angle of 30° with the horizontal. Another ball is simultaneously released from a point on the vertical line along the maximum height of the projectile. The initial height of the second ball is (g = 10 ms^-2)

• 6.25 m

• 2.5 m

• 1.25 m

• 5 m

If the two vectors $\overrightarrow{\mathrm{A}} = 2\hat{\mathrm{i}} + 3\hat{\mathrm{j}} + 4\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{B}} = \hat{\mathrm{i}} + 2\hat{\mathrm{j}} - \mathrm{n}\hat{\mathrm{k}}$ are perpendicular then the value of n is

• 1

• 2

• 3

• 4

A monkey climbs up and another monkey climbs down a rope hanging from a tree with same uniform acceleration separately. If the respective masses of monkeys are in the ratio 2 : 3, the common acceleration must be

• g/5

• 6g

• g/2

• g

From the top of tower, a stone is thrown up. It reaches the ground in t₁ second. A second stone thrown down with the same speed reaches the ground in t₂ second. A third stone released from rest reaches the ground in t₃ second. Then

• ${\mathrm{t}}_3 = \frac{\left({\mathrm{t}}_1 + {\mathrm{t}}_2\right)}{2}$

• ${\mathrm{t}}_3 = \sqrt{{\mathrm{t}}_1{\mathrm{t}}_2}$

• $\frac{1}{{\mathrm{t}}_3} = \frac{1}{{\mathrm{t}}_1} - \frac{1}{{\mathrm{t}}_2}$

• ${{\mathrm{t}}_3}^2 = {{\mathrm{t}}_2}^2 - {{\mathrm{t}}_1}^2$