Work And Energy Test

Result

Work And Energy Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

Two objects of masses 1 kg and 2 kg are moving along the same line and direction with velocities of 15 ms^–1 and 10 ms^–1, respectively. After they collide, the first object moves at a velocity of 10 ms^–1, the velocity of the second object is

A
15 ms^–1

B
12.5 ms^–1

C
10 ms^–1

D
8.5 ms^–1

Solution

m₁ = 1 kg m₂ = 2 kg u₁ = 15 m/s u₂ = 10 m/s
v₁ = 10 m/s v₂ = ?
According to law of conservation of momentum
m₁v₁+ m₂v₂= m₁u₁+ m₂u₂1 × 10 + 2 × v₂ = 1 × 15 + 2 × 10
By solving, v₂ = 12.5 m/s
Question 2
1 / -0

The momentum of a body increases by 20%. What is the percentage increase in its kinetic energy?

A
36%

B
44%

C
52%

D
60%

Solution

KE = ½ mv²
P = mv
Therefore, KE = ½ (mv)²/m = p²/(2m)
Considering the mass to be constant, if the momentum is increased by 20%, let the new momentum be P^/ = P + 0.2P = 1.2P.
New kinetic energy, KE^/ = (P^/)²/(2m)
=> KE^/= (1.2)²[P²/(2m)] = 1.44KE
=> (KE^/)/KE = 1.44
=> (KE^/ - KE)/KE = 0.44
=> (KE^/- KE)/KE × 100% = 44