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Question

A particle moving on a circular path with constant speed V, light is emitted from a projector at the centre of the circular path as shown in figure. The shadow of the particle is formed on the wall. The velocity of shadow up the wall is
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A
Vsec2ϕ
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B
Vcos2ϕ
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C
Vcosϕ
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D
Vsecϕ
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Solution

The correct option is A Vsec2ϕ
Let us assume r is the radius of the circular path and u be the velocity of the shadow
The position of the shadow on wall is given by
x=rtanϕ
Derivating w.r.t t on both sides of the equation,
ddt(x)=ddt(rtanϕ)
u=rsec2ϕdϕdt
Substituting ω=dϕdt in the above equation,
u=rωsec2ϕ
u=Vsec2ϕ
The velocity of the shadow up the wall is Vsec2ϕ


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