Which of the following has centre of mass not situated in the material of the body?

• A rod bent in the form of a circle

• Solid sphere

• Cricket bat

• None of the above

In a carnival ride, the passengers travel in a circle of radius 5.0 m, making one complete circle in 4.0 s. What is the acceleration?

• 24.6 m/s²

• 12.3 m/s²

• 6.15 m/s²

• 49.2 m/s²

A road is 8 m wide. Its radius of curvature is 40 m. The outer edge is above the lower edge by a distance of 1.2 m. This road is most suited for a velocity of

• 5.7 m/s

• 7.7 m/s

• 36.1 m/s

• 9.7 m/s

A 0.5 kg ball moves in a circle of radius 0.4 m at a velocity of 4 m/s. The centripetal force on the ball is

• 10 N

• 20 N

• 40 N

• 80 N

A rod of length L, whose lower end is sliding along the horizontal plane, starts to topple from the vertical position. The velocity of the upper end when it hits the ground is

• $\sqrt{\mathrm{gL}}$

• $\sqrt{3\mathrm{gL}}$

• $\sqrt{5\mathrm{gL}}$

• $3\sqrt{\mathrm{gL}}$

6.

Two bodies of moments of inertia I₁ and I₂ (I₁ > I₂) have equal angular momentum. If E₁ and E₂ are their kinetic energies of rotation, then

• E₁ > E₂

• E₁ = E₂

• E₁ < E₂

• Cannot be said

An artificial satellite revolves around the earth in a circular orbit with a speed v. If m is the mass of the satellite, its total energy is

• $\frac{1}{2}$mv²

• $\frac{-1}{2}$mv²

• -mv²

• $\frac{3}{2}$mv²

In an earth's satellite, the astronaut stands on a platform. His weight as indicated by the balance will be

• 6g

• 2g

• 8g

• zero

A body of mass m is moved to a height h equal to the radius of the earth. The increase in potential energy is

• 2mgR

• mgR

• $\frac{1}{2}\mathrm{mgR}$

• $\frac{1}{4}\mathrm{mgR}$

A particle moving with velocity (1/10)th of light will cross a nucleus in about

• 10^-8 s

• 10^-12 s

• 10^-47 s

• 10^-21 s