Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from to in 30 seconds. What is the speed of the object in km per hour ? [2010]

Question

Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from $\frac{25}{3} m$ to $\frac{50}{7} m$ in 30 seconds. What is the speed of the object in km per hour ? [2010]

Smart Achievers · Accepted Answer

(3)

$Using mirror formula for first position$

$u_{1} = ?, v_{1} = \frac{25}{3} cm, f = + 10 cm (= \frac{R}{2})$

$\frac{1}{v_{1}} + \frac{1}{u_{1}} = \frac{1}{f}, \frac{3}{25} + \frac{1}{u_{1}} = \frac{1}{10}$ $∴$ $u_{1} = - 50 cm$

$Using mirror formula for the second position$

$u_{2} = ?, v_{2} = \frac{50}{7} cm, f = 10 cm$

$\frac{1}{v_{2}} + \frac{1}{u_{2}} = \frac{1}{f}$ $\Rightarrow \frac{7}{50} + \frac{1}{u_{2}} = \frac{1}{10}$ $\Rightarrow \frac{1}{u_{2}} = \frac{1}{10} - \frac{7}{50}$

$∴$ $u_{2} = - 25 cm$

$Speed of object = \frac{u_{1} - u_{2}}{time} = \frac{25}{30} \times \frac{18}{5} = 3 {km h}^{- 1}$

Solution

Q.
Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from $\frac{25}{3} m$ to $\frac{50}{7} m$ in 30 seconds. What is the speed of the object in km per hour [2010]

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Solution

Q. Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from 253m to 507m in 30 seconds. What is the speed of the object in km per hour [2010]

Ans. (3) Using mirror formula for first position u1=?, v1=253cm, f=+10 cm(=R2) 1v1+1u1=1f, 325+1u1=110 ∴ u1=-50 cm Using mirror formula for the second position u2=?, v2=507cm, f=10 cm 1v2+1u2=1f⇒750+1u2=110⇒1u2=110-750 ∴ u2=-25 cm Speed of object=u1-u2time=2530×185=3 km h-1

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Q.
Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from $\frac{25}{3} m$ to $\frac{50}{7} m$ in 30 seconds. What is the speed of the object in km per hour [2010]