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General ScienceEasyAsked in: NDA · NDA-II 2018, GAT

If the focal length of a convex lens is 50 cm, which one of the following is its power?

  1. A.+2 dioptre
  2. B.+0.02 dioptre
  3. C.-0.5 dioptre
  4. D.+0.5 dioptre

Correct answer

A. +2 dioptre

Explanation

The correct answer is A, +2 dioptre. Power is the reciprocal of focal length in metres, and 50 cm is 0.5 m, so the power is 1 divided by 0.5, which is +2 dioptre. The power of a lens measures how strongly it bends light. Its SI unit is the dioptre, the power of a lens whose focal length is one metre. A convex or converging lens has a positive focal length and therefore a positive power, while a concave or diverging lens has a negative power. The shorter the focal length, the greater the power, which is why thick magnifying lenses are strong. Option B is wrong because +0.02 comes from dividing 1 by 50 without first converting centimetres into metres. Option C is wrong because a convex lens never has negative power, and the value is also wrong. Option D is wrong because 0.5 is the focal length in metres, not its reciprocal. Exam tip: P = 1/f with f in metres, or P = 100/f with f in centimetres; convex plus, concave minus.

Practice Questions

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Q1.General ScienceAsked in: NDA · NDA-II 2018, GATMedium

An object is placed in front of a convex mirror. Which one of the following statements is correct?

  1. A.It will never form an inverted image.
  2. B.The image moves towards the focus when the object moves towards the mirror.
  3. C.Depending on the position of the object with respect to the mirror, the image can be inverted and real.
  4. D.The size of the image becomes larger than that of the object when the object is placed at a distance equal to half the focal length.
Show answer
Correct answer: A. It will never form an inverted image.

For a real object anywhere in front of it, a convex mirror always gives a virtual, erect and diminished image.

Q3.General ScienceAsked in: NDA · NDA-II 2021, GATEasy

Three equal resistors are connected in parallel configuration in a closed electrical circuit. Then the total resistance in the circuit becomes

  1. A.one-third of the individual resistance.
  2. B.two-third of the individual resistance.
  3. C.equal to the individual resistance.
  4. D.three times of the individual resistance.
Show answer
Correct answer: A. one-third of the individual resistance.

For three equal resistors R in parallel, 1/Rp = 1/R + 1/R + 1/R = 3/R, so Rp = R/3.

Q4.General ScienceAsked in: NDA · NDA-I 2023, GATHard

Sand falls vertically on a conveyor belt at a rate of 0.1 kg/s. In order to keep the belt moving at a uniform speed of 2 m/s, the force required to be applied on the belt is :

  1. A.0 N
  2. B.0.2 N
  3. C.1.0 N
  4. D.2.0 N
Show answer
Correct answer: B. 0.2 N

The force needed equals the rate at which the belt must give horizontal momentum to the falling sand: F = v × (dm/dt) = 2 × 0.1 = 0.2 N. Newton's second law, in its general form, says force equals the rate of change of momentum.

Q5.General ScienceAsked in: NDA · NDA-I 2026, GATMedium

Consider the following statements in case of terrestrial planets : I. Mercury, Venus, Earth and Mars are terrestrial planets having low densities as compared to other planets. II. They lie between the Sun and the belt of asteroids. III. Their lower gravity can hold the escaping gases. Which of the statements given above is/are correct?

  1. A.I and II
  2. B.II and III
  3. C.I and III
  4. D.II only
Show answer
Correct answer: D. II only

The four terrestrial planets do lie between the Sun and the asteroid belt, but they are dense, not light, and their weak gravity could not hold on to escaping gases.