A bridge is in the form of a semi-circle of radius 40 m. The greatest speed with which a motor cycle can cross the bridge without leaving the ground at the highest point is (g =10 ms^-2) (Frictional force is negligibly small)

• 40 ms^-1

• 20 ms^-1

• 30 ms^-1

• 15 ms^-1

A ball of mass m is dropped from a height h on a platform fixed at the top of a vertical spring, as shown in figure. The platform is depressed by a distance x. Then the spring constant is

• $\frac{\mathrm{mg}}{\left(\mathrm{h} + \mathrm{x}\right)}$

• $\frac{\mathrm{mg}}{\left(\mathrm{h} + 2\mathrm{x}\right)}$

• $\frac{2\mathrm{mg} \left(\mathrm{h} + \mathrm{x}\right)}{{\mathrm{x}}^2}$

• $\frac{\mathrm{mg}}{\left(2\mathrm{h} + \mathrm{x}\right)}$

A ball dropped from a height of 2 m rebounds to a height of 1.5 m after hitting the ground. Then the percentage of energy lost is

• 25

• 30

• 50

• 100

A particle of mass m is moving in a horizontal circle of radius r, under a centripetal force $\mathrm{F} = \frac{\mathrm{k}}{{\mathrm{r}}^2}$, where k is a constant.

• The potential energy of the particle is zero

• The potential energy of the particle is $\frac{\mathrm{k}}{\mathrm{r}}$

• The total energy of the particle is $-\frac{\mathrm{k}}{2\mathrm{r}}$

• The kinetic energy of the particle is $- \frac{\mathrm{k}}{\mathrm{r}}$

A ring starts to roll down the inclined plane of height h without slipping. The velocity with which it reaches the ground is

• $\sqrt{\frac{1\mathrm{Ugh}}{7}}$

• $\sqrt{\frac{4\mathrm{gh}}{7}}$

• $\sqrt{\mathrm{gh}}$

• $\sqrt{2\mathrm{gh}}$

The angular momentum of a particle describing uniform circular motion is L. If its kinetic energy is halved and angular velocity doubled, its new angular momentum is

• 4 L

• $\frac{\mathrm{L}}{4}$

• $\frac{\mathrm{L}}{2}$

• 2 L

Two masses m₁ = 1 kg and m₂ = 2 kg are connected by a light inextensible string and suspended by means of a weightless pulley as shown in the figure.

Assuming that both the masses start from rest, the distance travelled by the centre of mass in 2s is (Take g = 10 ms^-2)

• $\frac{20}{9} \mathrm{m}$

• $\frac{40}{9} \mathrm{m}$

• $\frac{2}{3} \mathrm{m}$

• $\frac{1}{3} \mathrm{m}$

18.

A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 4R. The ratio of their respective periods is

• 4 : 1

• 1 : 8

• 8 : 1

• 1 : 4

A body is projected with a velocity of 2 x 11.2 kms^-1 from the surface of earth. The velocity of the body when it escapes the gravitational pull of earth is

• $\sqrt{3} \times 11.2 {\mathrm{kms}}^{-1}$

• 11.2 kms^-1

• $\sqrt{2} \times 11.2 {\mathrm{kms}}^{-1}$

• 6.5 × 11.2 kms^-1

The average depth of Indian ocean is about 3000 m. The fractional compression, $\frac{∆\mathrm{V}}{\mathrm{V}}$ of water at the bottom of the ocean (given that the bulk modulus of the water = 2.2 × 10² Nm^-2 and g = 10 ms^-2) is

• 0.82 %

• 0.91 %

• 1.36 %

• 1.24 %