Question

A plate of mass 10 gm is in equilibrium in air due to the force exerted by a light beam on plate. calculate power of beam. Assume the plate is perfectly absorbing.

A. $3 \times {10}^{7} W$
B. $3 \times {10}^{6} W$
C. $5.7 \times {10}^{7} W$
D.$2.22\times {10}^{7} W$

Answer 1

Hint: To solve this problem, first find the gravitational force acting on the plate. For doing this, use the formula for gravitational force. Substitute the values and calculate its value. Then, use the relationship between power and force to obtain the equation for force exerted by a light beam in terms of velocity and power. At equilibrium, gravitational force is equal to the force exerted by a light beam. Substitute the values and find the power of the light beam.

Complete answer:
Given: Mass of the plate (m)= 10 g= $10 \times {10}^{-3} kg$
Gravitational force acting on the plate is given by,
${F}_{gravitational}= mg$
Substituting values in above equation we get,
${F}_{gravitational}= 10 \times {10}^{-3} \times 10$
$\Rightarrow{F}_{gravitational}= {10}^{-1} N$ ...(1)
The relationship between power and force is given by,
$P= Fv$ ...(2)
Where, F is the force exerted
             v is the velocity of the object
Rearranging equation. (2) we get,
$F= \dfrac {P}{v}$ ...(3)
Here, the object is light. Light moves with velocity c. So, equation. (3) can be written as,
${F}_{light}= \dfrac {P}{c}$ ...(4)
At equilibrium, force exerted by the light beam should be equal to the gravitational force.
$\Rightarrow {F}_{light}= {F}_{gravitational}$
Substituting values in above equation we get,
$\dfrac {P}{c}= {10}^{-1}$
$\Rightarrow \dfrac {P}{3 \times {10}^{8}}= {10}^{-1}$
$\Rightarrow P= 3 \times {10}^{8} \times {10}^{-1}$
$\Rightarrow P= 3 \times {10}^{7}$
Hence, power of the beam is $3 \times {10}^{7}$ W.

So, the correct answer is option A i.e. $3 \times {10}^{7} W$.

Note:
Students should take care of the unit conversion. They should check whether the units are balanced or not. If not then they should convert the units of the quantities to their S.I. units. Not converting the units to their S.I. units will give them a wrong output altogether. Students should also take care of the powers while doing the calculations.