11.

A particle of mass M is situated at the centre of a spherical shell of same mass and radius a.The gravitational potential at a point situated  at a/2 distance  from the centre will be

• -3 GM/ a

• -2 GM/a

• -GM/a

• -GM/a

Six vectors and have the magnitudes and directions indicated in the figure. Which of the following statements is true?

A gramophone record is revolving with an angular velocity ω. A coin is placed at a distance r from the centre of the record. The static coefficient of friction is μ. The coin will revolve with the record if

• r = μgω²

• 
• 
• 

The dimension of , is permittivity of free space and E is electric field is 

• [ML²T^-2]

• [ML^-1T^-3]

• [ML²T^-1]

• [ML²T^-1]

A man of 50 kg mass standing in a gravity free space at height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 ms^-1. When the stone reaches the floor, the distance of the man above the floor will be

• 9.9 m

• 10.1 

• 10 m

• 10 m

The displacement of a particle along the x-axis is given by x = a sin² ωt. The motion of the particle corresponds to 

• simple of harmonic motion of frequency ω/π

• simple harmonic motion of frequency 3ω/2π

• non simple harmonic motion

• non simple harmonic motion

The period of oscillation of mass M suspended from a spring of negligible mass is T. If along with it another mass M is also suspended, the period of oscillation will now be

• T

• 

• 2T

• 2T

A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat Q in time t. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod when placed in thermal contact with the two reservoirs in time t?

• Q/4

• Q/16

• 2Q

• 2Q

A transverse wave os represented by y = A sin (ωt - kx). For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

• π A /2

•  π A

• 2πA

• 2πA

A tuning fork of frequency 512 Hz makes 4 beats/s with the vibrating string of a piano. The beat frequency decreases to 2 beats/s when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was.

• 510 Hz

• 514 Hz

• 516 Hz

• 516 Hz