A wheel starts rotating from rest at time t = 0 with a angular acceleration of 50 radians/s². The angular acceleration (α) decreases to zero value after 5 seconds. During this interval, a varies according to the equation

The angular velocity at t = 5 s will be

• 10 rad/s

• 250 rad/s

• 125 rad/s

• 100 rad/s

A communication satellite of 500 kg revolves around the earth in a circular orbit of radius 4.0 x 10⁷ m in the equatorial plane of the earth from west to east. The magnitude of angular momentum of the satellite is

• ∼ 0.13  × 10¹⁴ kg m² s^-1

• ∼ 1.3  × 10¹⁴ kg m² s^-1

• ∼ 0.58 × 10¹⁴ kg m² s^-1

• ∼ 2.58  × 10¹⁴ kg m² s^-1

The change in the gravitational potential energy when a body of mass m is raised to a height nR above the surface of the earth is ( here R is the radius of the earth )

• nn + 1 mgR

• nn - 1 mgR

• nmgR

• mgRn

A ball impinges directly on a similar ball at rest. The first ball is brought to rest by the impact. If half of the kinetic energy is lost by impact, the value of coefficient of restitution is

• 1 / 2√2

• 1 / √3

• 1 / √2

• √3 / 2

A transformer with efficiency 80% works at 4 kW and 100 V. If the secondary voltage is 200 V, then the primary and secondary currents are respectively

• 40 A and 16 A

• 16 A and 40 A

• 20 A and 40 A

• 40 A and 20 A

A projectile is given an initial velocity of î + 2 ĵ . The cartesian equation of its path is ( Take g = 10 ms² )

• y = x - 5x²

• y = 2x - 5x²

• y = 2x - 15x²

• y = 2x - 25x²

A physical quantity X is given by X =  The percentage error in the measurement of k, l,  m  and n are 1 %, 2%, 3% and 4% respectively. The value of X is uncertain by

• 8%

• 10%

• 12%

• None of these

Same spring is attached with  2 kg,  3 kg  and  1 kg blocks in three different cases as shown in figure. If  x₁ , x₂, x₃ be the extensions in the spring in the three cases, then

• x₁ = 0,  x₃ > x₂

• x₁ > x₂ > x₃

• x₃ > x₂ > x₁

• x₂ > x₁ > x₃

The figure shows a horizontal force F acting on a block of mass M on an inclined plane (angle θ).  What is the normal reaction N on the block?

• mg sinθ + F cosθ

• mg sinθ - Fcosθ

• mg cosθ - F sinθ

• mg cosθ + F sinθ

Assertion: If  α =  - 2t for a particle moving in a straight line starting with initial velocity 4 m/s from the origin, then distance travelled by it in 2 s is same as displacement.

Reason: Velocity changes direction after 2 s only.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.