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General ScienceMediumAsked in: NDA · NDA-II 2024, GAT

There is a ball of mass 320 g. It has 625 J potential energy when released freely from a height. The speed with which it will hit the ground is

  1. A.62.5 m/s
  2. B.2.0 m/s
  3. C.50 m/s
  4. D.40 m/s

Correct answer

A. 62.5 m/s

Explanation

The correct answer is A, 62.5 m/s. In free fall all the potential energy turns into kinetic energy, so 625 J = ½ × 0.32 kg × v², which gives v = 62.5 m/s.

First change the mass into kilograms: 320 g = 0.32 kg. When air resistance is ignored, mechanical energy is conserved, so the kinetic energy just before the ball hits the ground equals the potential energy it started with. Then ½mv² = 625 J, so v² = 2 × 625 ÷ 0.32 = 1250 ÷ 0.32 = 3906.25. The square root of 3906.25 is 62.5, so the ball strikes the ground at 62.5 m/s. As a check, ½ × 0.32 × 62.5 × 62.5 = 625 J.

B is wrong because 2.0 m/s would give a kinetic energy of only 0.64 J.

C is wrong because 50 m/s gives ½ × 0.32 × 2500 = 400 J, not 625 J.

D is wrong because 40 m/s gives 256 J, far less than 625 J.

Exam tip: for a free fall, mgh = ½mv², so v = √(2E/m); always convert grams to kilograms first.

Practice Questions

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Q1.General ScienceAsked in: CDS · CDS-I 2023, GKMedium

Which one of the following is not true for anodizing process?

  1. A.It makes aluminium corrosion resistant.
  2. B.Metals like aluminium, titanium and magnesium can be anodized.
  3. C.Clean aluminium article is the anode and oxygen gas is evolved at the cathode.
  4. D.It is used in aircraft industry.
Show answer
Correct answer: C. Clean aluminium article is the anode and oxygen gas is evolved at the cathode.

In anodizing the clean aluminium article is indeed the anode, but oxygen is released at the anode, not at the cathode; hydrogen is released at the cathode.

Q2.General ScienceAsked in: CDS · CDS-II 2016, GKMedium

Which one of the following statements is not correct?

  1. A.The response of the ear to sound of increasing intensity is approximately logarithmic.
  2. B.The sensitivity of the human ear does not vary with the frequency of the sound.
  3. C.When two or more waves traverse the same medium, the displacement of any element of the medium is the algebraic sum of the displacements due to each wave.
  4. D.Longitudinal waves can travel in all media—solids, liquids and gases.
Show answer
Correct answer: B. The sensitivity of the human ear does not vary with the frequency of the sound.

The statement that the sensitivity of the human ear does not vary with frequency is false, because the ear is far more sensitive to some frequencies than to others.

Q3.General ScienceAsked in: CDS · CDS-I 2017, GKEasy

Kwashiorkor disease in children is caused by

  1. A.sufficient carbohydrates but less fats in diet
  2. B.sufficient carbohydrates and fats but deficient proteins in diet
  3. C.sufficient vitamins but deficient fats in diet
  4. D.sufficient fats but deficient vitamins in diet
Show answer
Correct answer: B. sufficient carbohydrates and fats but deficient proteins in diet

Kwashiorkor is a disease of protein deficiency in a child who still gets enough calories. It usually appears when a child is weaned from breast milk onto a starchy diet with little protein.

Q4.General ScienceAsked in: CDS · CDS-I 2023, GKMedium

Which one of the following is the correct order of pH for the given substances?

  1. A.Coffee < Lemon juice < Milk of magnesia < Blood
  2. B.Milk of magnesia < Blood < Coffee < Lemon juice
  3. C.Lemon juice < Blood < Coffee < Milk of magnesia
  4. D.Lemon juice < Coffee < Blood < Milk of magnesia
Show answer
Correct answer: D. Lemon juice < Coffee < Blood < Milk of magnesia

Arranged from most acidic to most basic, the four substances fall in exactly this order. Lemon juice, rich in citric acid, has a pH of about 2 to 2.5.