A boy on a cycle pedals around a circle of 20 metres radius at a speed of 20 m/s. The combined mass of the body and the cycle makes with the vertical so that it may not fall is (g = 9.8 m/s² )

• 60.25^o

• 63.90^o

• 26.12^o

• 30.00^o

A car of mass 1000 kg moves on a circular track of radius 40 m. If the coefficient of friction is 1.28. The maximum velocity with which the car can be moved, is

• 22.4 m/s

• 112 m/s

• $\frac{0.64 \times 40}{1000 \times 100}$m/s

• 1000 m/s

A moving body of mass m and velocity 3 km/h collides with a rest body ofmass 2 m and stick to it. Now the combined mass starts to move. What will be the combined velocity?

• 4 km/h

• 1 km/h

• 2 km/h

• 3 km/h

A block B is pushed momentarily along a horizontal surface with an initial velocity v. If is the coefficient of vlicling friction between B and the surface, block B will come to rest after a time

• $\frac{\mathrm{v}}{\mathrm{g} \mathrm{\mu }}$

• $\frac{\mathrm{g} \mathrm{\mu }}{\mathrm{v}}$

• $\frac{\mathrm{g}}{\mathrm{v}}$

• $\frac{\mathrm{v}}{\mathrm{g}}$

A block slides down on an incline of angle 30° with an acceleration g/4 . Find the kinetic 4 friction coefficient.

• 1 / 2√2

• 0.6

• 1 / 2√3

• 1 / √2

A pendulum having a bob of mass m is hanging in a ship sailing along the equator form east to west. When the strip is stationary with respect to water, the tension in the string is T₀, The difference between T₀ and
earth attraction on the bob, is

• $\frac{\mathrm{mg} + \mathrm{m} {\mathrm{\omega }}^2 \mathrm{R}}{2}$

• $\frac{{\mathrm{m\omega }}^2 \mathrm{R}}{3}$

• $\frac{{\mathrm{m\omega }}^2 \mathrm{R}}{2}$

• mω² R

A ball of mass m hits the floor with a speed v making an angle of incidence θ with the normal. The coefficient of restitution is e. The speed of reflected ball and the angle of reflection of the ball will be

• v' = v, θ = θ'

• v' = $\frac{\mathrm{v}}{2}$, θ = 2θ'

• v' = 2v, θ = 2θ'

• v' = $\frac{3\mathrm{v}}{2}, \mathrm{\theta } = \frac{2\mathrm{\theta }\text{'}}{3}$

178.

A particle slides on surface of a fixed smooth sphere starting from top most point. The angle rotated by the radius through the particle, when it leaves contact with the sphere, is

• $\mathrm{\theta } ={\cos }^{-1} \frac{1}{3}$

• $\mathrm{\theta } = {\cos }^{-1} \left(\frac{2}{3}\right)$

• $\mathrm{\theta } = {\tan }^{-1} \left(\frac{1}{3}\right)$

• $\mathrm{\theta } = {\sin }^{-1} \frac{4}{3}$

A monkey of mass 15 kg is climbing on a rope with one end fixed to the ceiling. If it wishes to go up with an acceleration 1 m/s, how much force should it apply to the rope if rope is 5 m long and the monkey starts from rest?

• 150 N

• > 160 N

• 165 N

• 150 < T ≤ 160 N

A body weighing 8 g when placed in one pan and 18 g when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, then the true weight of the body is

• 13 g

• 9 g

• 22 g

• 12 g