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Work, Energy and Power

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Question 1
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A force straight F with rightwards arrow on top space equals space left parenthesis 5 straight i with hat on top space plus 3 straight j with hat on top space plus 2 straight k with hat on top right parenthesis space straight N is applied over a particle which displaces it from its origin to the straight r with rightwards arrow on top space equals space left parenthesis 2 straight i with hat on top minus straight j with hat on top right parenthesis space straight m.The work done on the particle in joules is

  • -7

  • +7

  • +10

  • +13

Solution

B.

+7

Work done in displacing the particle
straight W space equals space straight F with rightwards arrow on top space. straight r with rightwards arrow on top space equals space left parenthesis 5 straight i with hat on top space plus space 3 straight j with hat on top space plus 2 straight k with hat on top right parenthesis. left parenthesis 2 straight i with hat on top space minus straight j with hat on top right parenthesis space equals space 5 space straight x space 2 space plus 3 space straight x space left parenthesis negative 1 right parenthesis space plus space 2 straight x 0 space equals space 10 minus 3 equals space 7 straight J

Question 2
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A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. the work done by the force of gravity during the time the particle goes up is

  • 0.5 J

  • -0.5 J

  • −1.25 J

  • 1.25 J

Solution

C.

−1.25 J

negative mgh space equals negative space mg open parentheses fraction numerator straight v squared over denominator 2 straight g end fraction close parentheses space equals space minus space 1.25 space straight J
Question 3
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A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up ? Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g=9.8 ms−2:

  • 2.45 ×10−3 kg

  • 6.45 x×10−3 kg

  • 9.89 ×10−3 kg

  • 12.89 ×10−3 kg

Solution

D.

12.89 ×10−3 kg

Given potential energy burnt by lifting weight
= mgh = 10 x 9.8 x 1 x 1000 = 9.8 x 104 J
If mass lost by a person be m, then energy dissipated
 = m x 2 x 38 x 107 J /10
⇒ m = 5 x 10-3 x 9.8 / 3.8
= 12.89 x 10-3 kg 

Question 4
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A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is

  • 40 m/s

  • 20 m/s

  • 10 m/s

  • 10 square root of 30 m/s

Solution

A.

40 m/s

mgh space equals space 1 half mv squared straight v equals space square root of 2 gh end root space equals square root of 2 space straight x space 10 space straight x 80 end root space equals 40 space straight m divided by straight s
Question 5
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A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table?

  • 7.2 J

  • 3.6 J

  • 120 J

  • 1200 J 

Solution

B.

3.6 J

Mass per length
= M/L
= 4/2 = 2 kg/m
The mass of 0.6 m of chain = 0.6 x 2 = 1.2 kg
The centre of mass of hanging part = 0.6 +0 /2 = 0.3 m
Hence, work done in pulling the chain on the table
W =mgh
= 1.2 x 10 x 0.3
= 3.6 J

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