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Q.

Image of an object approaching a convex mirror of focal length 10 m along its principal axis is observed to move from $\frac{25}{3} m to \frac{50}{7} m$ in 1 minute. The average speed of the object in m/s, is ______________.

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a

$\frac{5}{6}$

b

$\frac{5}{12}$

c

$\frac{12}{5}$

d

$\frac{6}{5}$

answer is D.

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Detailed Solution

$\begin{array}{l} \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \\ \frac{3}{25} + \frac{1}{u_{1}} = \frac{1}{10} \\ \frac{1}{u_{1}} = \frac{1}{10} - \frac{3}{25} = \frac{0.5}{25} = - \frac{1}{50} \\ u_{1} = - 50 m \\ \frac{1}{u_{2}} = \frac{1}{10} - \frac{7}{50} = \frac{- 2}{50} \\ u_{2} = - 25 m \\ ∴ v = \frac{Δ u}{t} = \frac{25}{60} = \frac{5}{12} m / s \end{array}$

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Image of an object approaching a convex mirror of focal length 10 m along its principal axis is observed to move from 253 m to 507 m in 1 minute. The average speed of the object in m/s, is ______________.