A conducting sphere of radius 1O cm is charged with 10 μC. Another uncharged sphere of radius 20 cm is allowed to touch it for some time. After that if the spheres are separated, then surface density of charges on the spheres will be in the ratio of

• 1 : 4

• 1 : 2

• 1 : 3

• 1 : 1

If  v_ο be the orbital velocity of satellite in a circular orbit close to the earth's surface and  v_e  is the escape  velocity from the earth, then relation between the two is

• v_ο  = v_e

• v_e =  $\sqrt{3} {\mathrm{v}}_{\mathrm{o}}$

• v_e =  $\sqrt{2}$ v_ο

• v_e = 2 v_ο

Assertion:  Planet is a heavenly body revolving round the sun. 

Reason: Star is luminous body made of gaseous material.

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

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

• If the assertion is true but the reason is false.

• If both assertion and reason are false.

Assertion:  It is difficult to move a cycle along the road with its brakes on. 

Reason: Sliding friction is greater than rolling friction.

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

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

• If the assertion is true but the reason is false.

• If both assertion and reason are false.

Assertion:  In an elastic collision of two billiard balls, the total kinetic energy is conserved during the short time of oscillation of the balls (i.e. when they are in contact). 

Reason: Energy spent against friction does not follow the law of conservation of energy.

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

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

• If the assertion is true but the reason is false.

• If both assertion and reason are false.

Light propagates rectilinearly because of its

• frequency

• velocity

• Wavelength

• Wave nature

17.

What is the path difference for destructive interference?

• nλ

• $\frac{\left(\mathrm{n} + 1\right) \mathrm{\lambda }}{2}$

• n ( λ + 1)

• $\frac{\left(2\mathrm{n} + 1\right) \mathrm{\lambda }}{2}$

A siren emitting sound of frequency 800 Hz is going away from a static listener with a speed of 30 m/s. Frequency of the sound to be heard by the listener is (Take velocity of sound as 300 m/s)

• 733.3 Hz

• 481.2 Hz

• 644.8 Hz

• 286.5 Hz

A string in a musical instrument is 50 cm long and its fundamental frequency is 800 Hz. If a frequency of  1000 Hz is to be produced, then required length of string is

• 62.5 cm

• 40 cm

• 50 cm

• 37.5 cm

If equation of dound wave is   y = 0.0015 sin ( 62.8 x + 316 t ) then its wavelength will be

• 0.2 unit

• 0.3 unit

• 0.1 unit

• 2 unit