Question

An object (O) and a place mirror (M) are placed in the positions as shown in the figure. If the object and the mirror move simultaneously towards side in a straight path at uniform speeds of 2 cm $s^{-1}$ and 5 cm $s^{-1}$ respectively, find the shift in the position of the image of the object at the end of 10 seconds.

• A. $160$ cm
• B. $140$ cm
• C. $80$ cm
• D. $120$ cm

Answer 1

Answer: (C)

$80$ cm

Given: An object (O) and a place mirror (M) are placed in the positions as shown in the figure. If the object and the mirror move simultaneously towards side in a straight path at uniform speeds of $2cm{s}^{-1}$ and $5cm{s}^{-1}$ respectively,

To find the shift in the position of the image of the object at the end of 10 seconds.

Solution:

Fig(i) shows the position of object, image and mirror.

The object is moving at $2cm/s$, so after 10 sec, the object has moved by a distance of $2\times 10=20cm$ from original position.

The mirror is moving at $5cm/s$, so after 10 sec, the mirror has moved by a distance of $5\times 10=50cm$ from original position, as shown in fig(ii). That is ($50+20=70cm$) from the new object position (O').

So the new image formed will be at I' position = 70 cm behind the new mirror position (M').

So after 10 second the image of the object has moved by $(70+10=80cm)$ as shown in fig(ii).