Question
An object moves towards a convex lens of focal length 20
cm with a velocity of 5 cm/s. When the object is at 30 cm from the lens, find the rate at which the image is moving.Solution
Given:
- Focal length of convex lens, f = +20 cm
- Object distance at a given instant, u = –30 cm (object is in front ⇒ negative in sign convention)
- Object velocity: du/dt = +5 cm/s (since it's moving towards the lens, u is decreasing ⇒ du/dt is positive)
dv/dt = ?, i.e., rate of change of image position. Using lens formula: 1/v – 1/u = 1/f Differentiate both sides with respect to time t :
The image is moving away from the lens at a rate of 20 cm/s.
The circumference of a circle is 44 cm and the length of the rectangle is 4 times the radius of the circle. Find the area (in cm2) of the rec...
A square playground measure 1127.6164 meter2. If a man walks (49/20) m a minute, the time taken by him to walk one round around is approximat...
If the word PHOTOGRAPH is spelt with ‘F’ in place of ‘PH', then what would be the percentage reduction in the number of letters?
A cuboidal box with dimensions 12.5 cm (length), 7.5 cm (breadth), and 10 cm (height) is open from the top. The box is to be painted from the outside. I...
A rectangular tank is 50 meter long and 29meter deep. If 1000 cubic meters of water be drawn off the tank, the level of the water in the tank goes down ...
A rectangular piece of land has a perimeter of 88 metres and length of 20 metres. If the area of the land is to be divided into 6 equal portions, then w...
If tan θ + cot θ = 5, then the value of tan2 θ + cot2 θ + 2tan2 60° is:
What is the difference between (in m2) the area of a circular field of radius 14 metres and area of a rectangular piece of land having its di...
The perimeter of 3 squares is 30 cm, 36 cm and 42 cm respectively. What will be the area of the square having perimeter equal to sum of edges of 3 squar...
B is 25 percent more than C and C is 73 percent less than D. If B is 729, then what is the value of D?
Relevant for Exams:
