The Young's modulus of the material of a wire is 2 x 10¹⁰ Nm^–2. If the elongation strain is 1%, then the energy stored in the wire per unit volume (in Jm^–3) is

If Earth suddenly contracts to 1.5% of its present size, without any change in its mass, then how would the value of acceleration due to gravity change?

A bird flies for 4 s with a velocity of |t - 2| m/s in a straight line, where t = time in seconds. It covers a distance of

A cord is wound around the circumference of a bicycle wheel (without tyre) of diameter 1 m. A mass of 2 kg is tied to the end of the cord and it is allowed to fall from rest. The weight falls 2 m in 4 s. The axle of the wheel is horizontal and the wheel rotates with its plane vertical. The angular acceleration produced is (Take g = 10 ms^–2)

Match the following:

A body of mass 1 kg is projected with velocity 40 m/s at an angle of projection 30° with the horizontal. The magnitude of change in momentum from t = 0 to t = 2 sec is

A hollow metallic sphere, filled with water, is hung from a support by a long thread. A small hole is made at the bottom of the sphere and it is oscillated. How will the time period of oscillations be affected as water slowly flows out of the hole?

A car accelerates from rest at a constant rate ∝ for some time. Afterwards, it decelerates at a constant rate β to come to rest. If the total time elapsed is t , the maximum velocity acquired by the car is given by

A body is projected at time t = 0 from a certain point on a planet’s surface with a certain velocity at a certain angle with the planet’s surface (assumed horizontal). The horizontal and vertical displacements x and y (in metres), respectively vary with time t (in seconds) as x = 10 √3 t and y = 10 t – t².

What is the magnitude and direction of the velocity with which the body is projected?

A body of mass 0.4 kg is whirled in a vertical circle making 2 rev/s. If the radius of the circle is 1.2 m, then the tension in the string when the body is at the top of the circle is