The velocity of a particle is v = v₀ + gt + ft². If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

• v₀ + 2g + 3f

• v₀ + g/2 + f/3

• v₀ + g + f

• v₀ + g + f

A block of mass ‘m’ is connected to another block of mass ‘M’ by a spring (mass less) of spring constant ‘k’. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is stretched. Then a constant force ‘F’ starts acting on the block of mass ‘M’ to pull it. Find the force on the block of mass ‘m’.

• mF/M

• (M+m)F/m

• mF/(m+ M)

• mF/(m+ M)

If g_E and g_m are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan’s oil drop experiment could be performed on the two surfaces, one will find the ratio (electronic charge on the moon/ electronic charge on the earth) to be

• 1

• 0

• g_E/g_M

• g_E/g_M

A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α/R from the centre of the bigger disc.The value of α is

• 1/3

• 1/2

• 1/6

• 1/6

A round uniform body of radius R, mass M and moment of inertia ‘I’, rolls down (without slipping) an inclined plane making an angle θ with the horizontal. Then its acceleration is

Angular momentum of the particle rotating with a central force is constant due to

• Constant Force

• Constant linear momentum

• Zero Torque

• Zero Torque

A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10,000. N/m. The spring compresses by

• 5.5 cmYes

• 2.5 cm

• 11 cm

• 11 cm

A particle is projected at 60° to the horizontal with a kinetic energy K. The kinetic energy at the highest point is 

• K

• 0

• K/2

• K/2

9.

The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 × 10^-2 cos πt metres. The time at which the maximum speed first occurs

• 0.5 s

• 0.75 s

• 0.125 s

• 0.125 s

A point mass oscillates along the x-axis according to the law x = x₀ cos (ωt - π/4). If the acceleration of the particle is written as a = A cos (ωt + δ), then

• A = x₀ , δ = – π/4

• A = x₀ ω₂ , δ = π/4 

• A = x₀ ω₂, δ = –π/4 

• A = x₀ ω₂, δ = –π/4