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Question

In the figure shown, two plane mirrors M1 and M2 are fixed on the two blocks A and B as shown in the figure. An object is placed midway between the two mirrors . Find the acceleration of the image formed by mirror-2 w.r.t the image formed by mirror-1.

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Solution

The correct option is **D** 44g15

Acceleration of the mirror M1 is given by

a1=−4mg5m=−4g5

Acceleration of the block M2 is given by

a2=2mg3m=2g3

Let I1 and I2 be the images formed by M1 and M2 respectively.

Acceleration of I1 w.r.t O is

→aI1=2→a1=−8g5

[since O is stationary and M1 is moving away with acceleration a1]

Acceleration of I2 w.r.t O is

−→aI2=2→a2=4g3

Thus, Acceleration of image formed by mirror 2 w.r.t to image formed by mirror 1 is given by

−−→aI2I1=−→aI2−−→aI1

=4g3−(−8g5)

or −−→aI2I1=44g15 (towards right - +ve)

Acceleration of the mirror M1 is given by

a1=−4mg5m=−4g5

Acceleration of the block M2 is given by

a2=2mg3m=2g3

Let I1 and I2 be the images formed by M1 and M2 respectively.

Acceleration of I1 w.r.t O is

→aI1=2→a1=−8g5

[since O is stationary and M1 is moving away with acceleration a1]

Acceleration of I2 w.r.t O is

−→aI2=2→a2=4g3

Thus, Acceleration of image formed by mirror 2 w.r.t to image formed by mirror 1 is given by

−−→aI2I1=−→aI2−−→aI1

=4g3−(−8g5)

or −−→aI2I1=44g15 (towards right - +ve)

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