A point object is moving on the principal axis

Asked by admin @ 13/08/2021 in Physics viewed by 325 People

A point object is moving on the principal axis of

concave mirror of focal length 24 cm towards themirror. When it is at a distance of 60 cm fromthe mirror, its velocity is 9 cm/s. What is thevelocity of the image at that instant :(a) 5 cm/s towards mirror(b) 4 cm/s towards mirror(c) 4 cm/s away from mirror(d) 9 cm/s away from mirror

Answered by admin @ 13/08/2021

Given :

A point object is moving towards a concave mirror on its principal axis .

Focal length of the concave mirror :

f = -24 cm , since focal length is negative for concave mirror

Velocity of object when it is at a distance of 60 cm from the mirror :

$v_{obj}$ = 9 $\frac{cm}{s}$

To Find :

Velocity of the image at the given instant = ?

Solution :

Here 1st we have to find the distance of image from the mirror .

From the mirror formula we have :

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\\$ -(1)

So using this formula we can have the v i.e. distance of image as :

$\frac{1}{v} = \frac{-1}{24}+\frac{-1}{60} \\$

On solving this we get v = -40 cm

On differentiating eq 1 we get :

$\frac{-1}{v^{2}} .\frac{dv}{dt} - \frac{1}{u^{2} }. \frac{du}{dt} = o\\$

Or, $\frac{1}{v^{2}} .\frac{dv}{dt} + \frac{1}{u^{2} }. \frac{du}{dt} = o\\$

Or, $\frac{v_{i}}{40^{2} } +\frac{9}{60^{2} } = 0$

Or, $v_{i} = \frac{-9}{60^{2} } \times 40^{2}$

⇒ $v_{i$ = $-4 \frac{m}{s}$

So the velocity of image at the given instant is 4 cm per s towards the mirror .

Hence correct option is (b). 4 cm per sec towards the mirror .

A point object is placed on the principal axis

Asked by admin @ 20/08/2021 in Physics viewed by 379 persons

A point object is placed on the principal axis of a convex lens (f = 15 cm) at a distance of 30 cm from it. A glass plate (μ = …

The position of an object moving along x axis

Asked by admin @ 11/08/2021 in Physics viewed by 331 persons

Q. The position of an object moving along x-axis is given by x= a + bt2 where a=8.5m, b=2.5m/s2 and t is measured in seconds. What is its velocity at …

An object is placed perpendicular to the principal axis

Asked by admin @ 11/08/2021 in Physics viewed by 281 persons

An object is placed perpendicular to the principal axis of a convex lens of focal length 20cm. the distance of the object from the lens is 30cm. find the 1)position …

At what point or points on the x-axis is the electric potential zero?

Asked by maham237 @ 30/11/2020 in Physics viewed by 371 persons

a +3.0 nc charge is at x=0 cm and a -1.0nc charge is at x=4cm.

A proton moves along the x-axis with vx=1.0×107m/s.

Asked by maham237 @ 22/12/2020 in Mathematics viewed by 533 persons

A proton moves along the x-axis with vx=1.0×107 m/s. As it passes the origin, what are the strength and direction of the magnetic field at the (x, y, z) positions …

The point (4, 3) is reflected across the x-axis. in what quadrant will the new coordinate be?

Asked by maham237 @ 08/01/2021 in Mathematics viewed by 425 persons

What causes an object to move in a circular path

Asked by admin @ 08/11/2021 in Physics viewed by 295 persons

A centripetal force causes circular motion because it accelerates an object

The energy transferred by a force to a moving object

Asked by admin @ 07/10/2021 in Physics viewed by 248 persons

The energy transferred by a force to a moving object?

An object moving with a speed of 6.25

Asked by admin @ 31/08/2021 in Physics viewed by 300 persons

An object moving with the speed of 6.25 m/s is decelerated at a rate given by dv/dt = -2.5 √v where v is the instantaneous speed . the time taken …

Abscissa of all points on x axis is

Asked by admin @ 26/08/2021 in Math viewed by 334 persons

What is the abscissa of all the point on the x axis

Abscissa of all points on y axis is

Asked by admin @ 25/08/2021 in Math viewed by 288 persons

Abscissa of all points on y axis

The inertia of a moving object depends on

Asked by admin @ 24/08/2021 in Physics viewed by 346 persons

Inertia of a moving object depends upon ? a.momentum b. Speed c. Shape d. Mass MCQ

Give one example where force moves a stationary object

Asked by admin @ 20/08/2021 in Physics viewed by 306 persons

Give one example where force move a stationary object

A point mass starts moving in a straight line

Asked by admin @ 20/08/2021 in Physics viewed by 293 persons

a point mass starts moving in a straight line with constant acceleration "a". at a point after the beginning of motion,the acceleration changes sign, without change in magnitude. determine time …