A point object is moving on the principal axi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For a concave mirror,the mirror formula is given by $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$.Given: Focal length $f = -24\;cm$ (sign convention f

Vedclass · Accepted Answer

$4\;cm/sec$ towards the mirror

Vedclass · Answer

(C) For a concave mirror,the mirror formula is given by $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$.Given: Focal length $f = -24\;cm$ (sign convention for concave mirror),object distance $u = -60\;cm$.Substituting the values: $\frac{1}{-24} = \frac{1}{v} + \frac{1}{-60}$.$\frac{1}{v} = \frac{1}{60} - \frac{1}{24} = \frac{2 - 5}{120} = \frac{-3}{120} = -\frac{1}{40}$.So,$v = -40\;cm$.Differentiating the mirror formula with respect to time $t$: $-\frac{1}{v^2} \frac{dv}{dt} - \frac{1}{u^2} \frac{du}{dt} = 0$.Therefore,the velocity of the image $v_i = \frac{dv}{dt} = -(\frac{v}{u})^2 \frac{du}{dt}$.Given $\frac{du}{dt} = -9\;cm/s$ (moving towards the mirror).$v_i = -(\frac{-40}{-60})^2 	imes (-9) = -(\frac{2}{3})^2 	imes (-9) = -(\frac{4}{9}) 	imes (-9) = 4\;cm/s$.The positive sign indicates the image is moving in the same direction as the object,which is towards the mirror.

$A$ point object is moving on the principal axis of a concave mirror of focal length $24\;cm$,towards the mirror. When it is at a distance of $60\;cm$ from the mirror,its velocity is $9\;cm/sec$. What is the velocity of the image at that instant?

Similar Questions

$A$ car is fitted with a convex side-view mirror of focal length $20\ cm$. $A$ second car $2.8\ m$ behind the first car is overtaking the first car at a relative speed of $15\ m/s$. The speed of the image of the second car as seen in the mirror of the first one is

$A$ point object on the principal axis at a distance $1.5\, cm$ in front of a concave mirror of radius of curvature $20\, cm$ has velocity $2\, mm/s$ perpendicular to the principal axis. The velocity of image at that instant will be.....$mm/s$

An object approaches a convex mirror of radius of curvature $20 \,m$ along its optical axis. The image is observed to move from $\frac{25}{3} \,m$ to $\frac{50}{7} \,m$ from the mirror in $30 \,s$. What is the speed of the object in $km/h$?

The bob of a pendulum is released from position $P$. What is the velocity of the image of the bob on the mirror $M$ at position $Q$ with respect to the bob?

$A$ luminous point object is moving along the principal axis of a concave mirror of focal length $12 \ cm$ towards it. When its distance from the mirror is $20 \ cm$,its velocity is $4 \ cm/s$. The velocity of the image in $cm/s$ at that instant is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module