WORK ENERGY AND POWER

6 )

The force constant of a wire is K and that of the another wire is 3k when both the wires are stretched through same distance, if work done are W₁ and W₂, then...

Select correct option from following options

(A) w₂ = 3w₁² (B) W₂ = 0.33W₁

View Solution

Answer :

Workdone = W = (1/2)Kx²

for both wires distance is same

W ∝ K

{(W₁) / (W₂)} = {(K₁) / (K₂)} = {K / (3K)} = (1 / 3)

W₂ = 3W₁

7 )

A ball is released from the top of a tower. What is the ratio of work done by force of gravity in first, second and third second of the motion of the ball ? [h_n α (2n – 1)]

1 : 2 : 3

1 : 4 : 9

1 : 3 : 5

1: 5 : 3

View Solution

Answer :

Given h_n α (2n – 1)

W = F × s

W α s

i.e. W α h

W₁ : W₂ : W3 = h₁ : h₂ : h₃

= (2 – 1) : (4 – 1) : (6 – 1)

= 1 : 3 : 5

8 )

A spring of spring constant 10³ N/m is stretched initially 4 cm from the unscratched position. How much the work required to stretched it further by another 5 cm ?

6.5 NM

2.5 NM

3.25 NM

6.75 NM

View Solution

Answer :

W = (1/2)Kx²

here W = (1/2)K {(x₂²) – (x₁²)}

= (1/2) × 10³ × {(x₂²) – (x₁²)}

spring is stretched from unstreched position to 4 cm and further 5 cm

hence x₂ = 9cm

x₁ = 4cm

∴ W = (1/2) × 10³ (9² – 4²)10^–4

= {(0.1) / 2} × 65

= 3.25 N – M

9 )

The mass of a car is 1000 kg. How much work is required to be done on it to make it move with a speed of 36 km/h?

Select correct option from following options

(A) 2.5 × 10⁴ J (B) 5 × 10³ J

View Solution

Answer :

KE = (1/2)mV²

= (1/2) × 1000 × {(36 × 1000) / (3600)}²

= 500 × 100

= 5 × 10⁴J

10 )

A body of mass 6 kg is under a force, which causes a displacement in it given by S = [(2t³) / 3] (in m). Find the work done by the force in first one seconds.

2 J

3.8 J

5.2 J

24 J

View Solution

Answer :

m = 6 kg

t = 1 s

s = {(2t³) / 3}

V = {(ds) / (dt)} = (2/3) × 3t² = 2t²

a = {(dv) / (dt)} = 4t hence at t = 1, a = 4

W = _o∫^t F ∙ ds

= _o∫^t (m × a) ds

= _o∫^t 6 × 4 ds

= 24 [s]_o^t

= 24 (t – o)

= 24 × 1 = 24J

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