A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as v= α√x . The displacement of the particle varies with time as

• t³

• t²

• t

• t

A bomb of mass 16 kg at rest explodes into two pieces of masses of 4 kg and 12 kg. The velocity of the 12 kg mass is 4 ms⁻¹ . The kinetic energy of the other mass is

• 144 J

• 96 J

• 288 J

• 288 J

3.

A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of 45° with the initial vertical direction is

• 
• 
• 
• 

A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. the work done by the force of gravity during the time the particle goes up is

• 0.5 J

• -0.5 J

• −1.25 J

• −1.25 J

The potential energy of a 1 kg particle free move along the x-axis is given by

The total mechanical energy of the particle 2 J. Then, the maximum speed (in m/s) is

• 2

• 
• 
• 

A force of  acts on O, the origin of the coordinate system. The torque about the point (1, −1) is

A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity ω. Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ω′

The rms value of the electric field of the light coming from the Sun is 720 N/C. The average total energy density of the electromagnetic wave is

• 3.3 × 10⁻³ J/m³

• 4.58 × 10⁻⁶ J/m³

• 6.37 × 10⁻⁹ J/m³

• 6.37 × 10⁻⁹ J/m³

Four point masses, each of value m, are placed at the corners of a square ABCD of side A. The moment of inertia through A and parallel to BD is

• m

• 2m

• √m

• √m

A wire elongates by 

• 2

• 2