Question

A spherical mirror forms image of a point object placed principal Axis at a distance 10cm at distance 30 cm from the mirror. if object start moving with velocity 9 cm/sec. find initial velocity of the image
-9cm
-4cm
-1cm
-3cm​

Answer 1

GIVEN :-

A spherical mirror forms image of a point object placed principal Axis at a distance 10cm at distance 30 cm from the mirror. object starts moving with velocity 9 cm/sec.

TO FIND :-

initial velocity of the image .

SOLUTION:-

V = -10 cm

u = -30 cm

We know ,

$\rightarrow \: \frac{dy}{dx} = \frac{ - v {}^{2} }{u {}^{2} } . \: \frac{du}{dt} \\ \\ \\ \implies \: \frac{dv}{dt} = \: \frac{ - 100}{900} . \frac{du}{dt } \\ \\ \\ \implies \: \frac{du}{dt} = 9 \: \frac{cm}{s} . \\ \\ \\ \\ \rightarrow \: \frac{dv}{dt} = \frac{ - 1}{9} \times 9 = - 1$

Hence , Answer is , -1cm/s. Option(C)

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HOPE IT HELPS :)

Answer 2

AnswEr :

• Initial velocity of the object is -1 cm/s . [Option 3]

GivEn :

• Image distance (v) = -10 cm

• Object distance (u) = -30 cm

• Velocity of the object = 9 cm/sec

To find :

• Initial velocity of the object = ?

Formula usEd :

Besides lens formula , their are many other formulas to calculate such values!

For the above question we can use differential calculus formulas .

It is given as ,

$\large \dag \: { \boxed{ \sf{ \blue{\dfrac{dy}{dx} = \dfrac{ - {v}^{2} }{ {u}^{2} } \times \dfrac{du}{dt} }}}}$

SoluTion :

According to the formula,

$\sf : \implies \: \: \: {\dfrac{dy}{dx} = \dfrac{ - {v}^{2} }{ {u}^{2} } \times \dfrac{du}{dt}}$

$\sf : \implies \: \: \: {\dfrac{dv}{dt} = \dfrac{ - {v}^{2} }{ {u}^{2} } \times \dfrac{du}{dt}}$

$\sf : \implies \: \: \: {\dfrac{dv}{dt} = \dfrac{ - {10}^{2} }{ {9}^{2} } \times \dfrac{du}{dt}}$

$\sf : \implies \: \: \: {\dfrac{dv}{dt} = \dfrac{ - {100} }{ 900 } \times \dfrac{du}{dt}}$

$\sf : \implies \: \: \: {\dfrac{dv}{dt} = \dfrac{ - {1} }{ 9 } \times \dfrac{du}{dt}}$

$\sf : \implies \: \: \: {\dfrac{dv}{dt} = \dfrac{ - {1} }{ 9 } \times 9}$

$\sf : \implies \: \: \: {\dfrac{dv}{dt} = - 1} \: cm/s$

Therefore, initial velocity of the object is -1 cm/s . [Option 3]