A small block of mass m and a concave mirror of radius R fitted with a stand, lie on a smooth horizontal table with a separation d between them. The mirror together with its stand has a mass m. The block is pushed at t = 0 towards the mirror so that it starts moving towards the mirror at a constant speed V and collides with it. The collision is perfectly elastic. Find the velocity of the image
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. t < 
u = – (d – Vt)
f = 
We know that 
= – m 2 
Here, m = 
= 
= 
∴ v 1 = velocity of image = – 
v
= 
Fig. Fig.
t > 
Block will collide with mirror assembly after time T = 
.
From conservation of linear momentum, block and mirror assembly will exchange their momentum i.e., block will stop and mirror starts moving with velocity V.
u = – V 
Also, m = 
= 
We know that 
= – m 2 
or 
– 
= m 2 ( 
)
Let us assume rightward direction as positive
v 1 – V = – m 2 (– V)
or v 1 = (1 + m 2 )V
∴ v 1 = V 
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems