A 100 W light bulb is placed at the centre of a spherical chamber of radius 0.10 m. Assume that 66 % of the energy supplied to the bulb is converted into light and that the surface of chamber is perfectly absorbing. The pressure exerted by the light on the surface of the chamber is

Question

A 100 W light bulb is placed at the centre of a spherical chamber of radius 0.10 m. Assume that 66 % of the energy supplied to the bulb is converted into light and that the surface of chamber is perfectly absorbing. The pressure exerted by the light on the surface of the chamber is (A) 0.87 × 10-6 Pa (B) 1.77 × 10-6 Pa (C) 3.50 × 10-6 Pa (D) None of the above

Tardigrade Admin · Accepted Answer

Light falling per second on the surface of sphere

E = \frac{66}{100} \times 100 = 66 W

Momentum of the light falling per second on the surface of sphere

= \frac{E}{c}

Momentum of the reflected light

= 0;

as the light is completely absorbed.
Force exerted by light,

F = \frac{E}{c} - 0 = \frac{E}{c}

Pressure on surface,

p = \frac{F}{4 π r ^{2}} = \frac{E / c}{4 π r ^{2}}

= \frac{66/ ( 3 \times 1 0 ^{8} )}{4 \times ( 22/7 ) \times ( 0.10 ) ^{2}}

= 1.75 \times 1 0^{- 6} P a

Q. A $100 W$ light bulb is placed at the centre of a spherical chamber of radius $0.10 m$ . Assume that $66%$ of the energy supplied to the bulb is converted into light and that the surface of chamber is perfectly absorbing. The pressure exerted by the light on the surface of the chamber is

$0.87 \times 1 0^{- 6} P a$

$1.77 \times 1 0^{- 6} P a$

$3.50 \times 1 0^{- 6} P a$

None of the above

Q. A 100W light bulb is placed at the centre of a spherical chamber of radius 0.10m. Assume that 66% of the energy supplied to the bulb is converted into light and that the surface of chamber is perfectly absorbing. The pressure exerted by the light on the surface of the chamber is

0.87×10−6Pa

1.77×10−6Pa

3.50×10−6Pa

None of the above

Q. A $100 W$ light bulb is placed at the centre of a spherical chamber of radius $0.10 m$ . Assume that $66%$ of the energy supplied to the bulb is converted into light and that the surface of chamber is perfectly absorbing. The pressure exerted by the light on the surface of the chamber is

$0.87 \times 1 0^{- 6} P a$

$1.77 \times 1 0^{- 6} P a$

$3.50 \times 1 0^{- 6} P a$