A 4 kg roller is attached to a massless spring of spring constant k = 100 N/m. It rolls without slipping along a frictionless horizontal road. The roller is displaced from its equilibrium position by 10 cm and then released. Its maximum speed will be

• 0.5 m s^-1

• 0.6 m s^-1

• 0.4 m s^-1

• 0.8 m s^-1

A particle is thrown vertically upwards with velocity 11.2 km s1 from the surface of earth. Calculate its velocity at height 3 R. Where R is the radius of earth

• $\simeq$ 9.25 km s^-1

• $\simeq$ 5.6 km s^-1

• $\simeq$ 11.2 km s^-1

• $\simeq$ 4.3 km s^-1

If 2 kg mass is rotating on a circular path of radius 0.8 m with angular velocity of 44 rad/sec. If radius of the path becomes 1 m, ther what will be the value of angular velocity?

• 28.16 rad/sec

• 19.28 rad/sec

• 8.12 rad/sec

• 35.26 rad/sec

Find out the correct relation for the dependance of change in acceleration due to gravity on the angle at the latitude, due to rotation of earth

• dg ∝ cos$\mathrm{\varphi }$

• dg ∝ cos²$\mathrm{\varphi }$

• dg ∝ cos^3/2$\mathrm{\varphi }$

• dg ∝ $\frac{1}{\mathrm{cos\varphi }}$

A solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclined plane. Which of the following will have maximum acceleration at the bottom of the plane?

• Circular disc

• Solid cylinder

• Solid sphere

• Hollow cylinder

Calculate the heat emitted by a bulb of 100 W in 1 min.

• 100 J

• 1000 J

• 600 J

• 6000 J

Assertion: Animate object can accelerate in the absence of external force. 

Reason:  Newton's second law is not applicable on animate object.

• 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 is false.

Assertion:  In elastic collision, kinetic energy is conserved. 

Reason:  Energy is always conserved.

• 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 assertion is true but reason is false.

Dimensional formula of ΔQ, heat supplied to the system is given by

• [ M¹ L² T^-2 ]

• [ M¹ L¹ T^-2 ]

• [ M¹ L² T^-1 ]

• [M¹ L¹ T^-1 ]

A spherical body of diameter D is falling in viscous medium. Its terminal velocity is proportional to

• V_t ∝ D^1/2

• V_t ∝ D^3/2

• V_t ∝ D²

• V_t ∝ D^5/2