The quantity which has the same dimensions as that of gravitational potential is

• latent heat

• impulse

• angular acceleration

• Planck's constant

The percentage error in measuring M, L and T are 1 %, 1.5% and 3% respectively. Then the percentage error in measuring the physical quantity with dimensions [ML^-1 T^-1] is

• 1 %

• 3.5 %

• 5.5 %

• 4.5 %

From an elevated point P, a stone is projected vertically upwards when the stone reaches a distance h below P, its velocity is double of its velocity at a height h above P. The greatest height attained by the stone from the point of projection is

• $\frac{3}{5} \mathrm{h}$

• $\frac{5}{3} \mathrm{h}$

• $\frac{5}{7} \mathrm{h}$

• $\frac{2}{3} \mathrm{h}$

The distance x covered by a particle varies with time t as x² = 2t² + 6t + 1. Its acceleration varies with x as

• x

• x²

• x^-1

• x^-3

A particle describes uniform circular motion in a circle of radius 2 m, with the angular speed of 2 rad s^-1. The magnitude of the change in its velocity in $\frac{\mathrm{\pi }}{2}$ s is

• 0 ms^-1

• $2\sqrt{2} {\mathrm{ms}}^{-1}$

• 8 ms^-1

• 4 ms^-1

A body projected at an angle with the horizontal has a range 300 m. If the time of flight is 6 s, then the horizontal component of velocity is

• 30 ms^-1

• 50 ms^-1

• 40 ms^-1

• 45 ms^-1

A constant force F acts on a particle of mass 1 kg moving with a velocity v, for one second. The distance moved in that time is

• 0

• $\frac{\mathrm{F}}{2}$

• $\mathrm{v} + \frac{\mathrm{F}}{2}$

• 2F

The velocity-time graph for the vertical component of the velocity of a body thrown upwards from the ground and landing on the roof of a building is given in the figure. The height of the building is

• 50 m

• 40 m

• 20 m

• 30 m

A spacecraft of mass 100 kg breaks into two when its velocity is 10⁴ ms^-1. After the break, a mass of 10 kg of the spacecraft is left stationary. The velocity of the remaining part is

• 10³ ms^-1

• 11.11 × 10³ ms^-1

• 11.11 × 10² ms^-1

• 10⁴ ms^-1

A particle tied to a string describes a vertical circular motion of radius r continually. If it has a velocity $\sqrt{3\mathrm{gr}}$ at the highest point, then the ratio of the respective tensions in the string holding it at the highest and lowest points is

• 4 : 3

• 5 : 4

• 1 : 4

• 3 : 2