The percentage errors in the measurement of length and time period of a simple pendulum are 1% and 2% respectively. Then the maximum error in the measurement of acceleration due to gravity is

• 8 %

• 3 %

• 5 %

• 6 %

Dimensional formula of Stefan's constant is

• [MT^-3K^-4]

• [MLT^-2K^-4]

• [ML²T^-2]

• [MT^-2L⁰]

A body is falling freely under gravity. The distances covered by the body in first, second and third minute of its motion are in the ratio

• 1 : 4 : 9

• 1 : 2 : 3

• 1 : 3 : 5

• 1 : 5 : 6

A bullet fired into a fixed wooden block loses half of its velocity after penetrating 40 cm. It comes to rest after penetrating a further distance of

• $\frac{22}{3} \mathrm{cm}$

• $\frac{40}{3} \mathrm{cm}$

• $\frac{20}{3} \mathrm{cm}$

• $\frac{22}{5} \mathrm{cm}$

A ball A is thrown up vertically with a speed u and at the same instant another ball B is released from a height h. At time t, the speed of A relative to B is 

• u

• 2u

• u − gt

• $\sqrt{\left({\mathrm{u}}^2 - \mathrm{gt}\right)}$

A bullet is to be fired with a speed of 2000 ms^-1 to hit a target 200 m away on a level ground. If g = 10 ms^-2, the gun should be aimed

• directly at the target

• 5 cm below the target

• 5 cm above the target

• 2 cm above the target

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

A stationary body of mass 3 kg explodes into three equal pieces. Two of the pieces fly off in two mutually perpendicular directions, one with a velocity of $3 \hat{\mathrm{i}}$ ms^-1 and the other with a velocity of $4 \hat{\mathrm{j}}$ ms^-1. If the explosion occurs in 10^-4  s, the average force acting on the third piece in newton is

• $\left(3\hat{\mathrm{i}} + 4\hat{\mathrm{j}}\right) \times {10}^{-4}$

• $\left(3\hat{\mathrm{i}} - 4\hat{\mathrm{j}}\right) \times {10}^{-4}$

• $\left(3\hat{\mathrm{i}} + 4\hat{\mathrm{j}}\right) \times {10}^4$

• $- \left(3\hat{\mathrm{i}} + 4\hat{\mathrm{j}}\right) \times {10}^4$

A mass of 1 kg is just able to slide down the slope of an inclined rough surface when the angle of inclination is 60°. The minimum force necessary to pull the mass up the inclined plane (g = 10 ms^-2) is

• 14.14 N

• 17.32 N

• 10 N

• 16.66 N