Work Energy and Power Chapter-Wise Test 6

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A \( 5 \, \text{kg} \) mass at \( 20 \, \text{m/s} \) collides elastically with an identical stationary mass. What is the speed of the first mass after collision?

For equal masses in elastic collision, \( v_{1f} = 0 \, \text{m/s} \) (first mass stops).

0 m/s
5 m/s
10 m/s
15 m/s
1

A \( 3 \, \text{kg} \) object is dropped from \( 17 \, \text{m} \). What is its speed just before hitting the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Potential energy \( V = mgh = 3 \times 10 \times 17 = 510 \, \text{J} \).

Kinetic energy \( \frac{1}{2} m v^2 = 510 \Rightarrow v^2 = 340 \Rightarrow v = \sqrt{340} \approx 18.44 \, \text{m/s} \).

18 m/s
18.4 m/s
19 m/s
19.5 m/s
2

A \( 8 \, \text{kg} \) mass is lifted \( 4 \, \text{m} \) in \( 2.5 \, \text{s} \) at constant speed. What is the power? (Take \( g = 10 \, \text{m/s}^2 \))

Work \( W = mgh = 8 \times 10 \times 4 = 320 \, \text{J} \).

Power \( P = \frac{W}{t} = \frac{320}{2.5} = 128 \, \text{W} \).

120 W
128 W
135 W
140 W
2

A \( 900 \, \text{kg} \) car at \( 14 \, \text{m/s} \) hits a spring (\( k = 6 \times 10^3 \, \text{N/m} \)). What is the maximum compression?

Initial \( K = \frac{1}{2} \times 900 \times 14^2 = 88200 \, \text{J} \).

Spring energy \( \frac{1}{2} k x_m^2 = 88200 \Rightarrow 3000 x_m^2 = 88200 \Rightarrow x_m = \sqrt{29.4} \approx 5.42 \, \text{m} \).

5.2 m
5.4 m
5.6 m
5.8 m
2

A \( 6 \, \text{kg} \) block slides down a frictionless incline from \( 10 \, \text{m} \) height. What is its speed at the bottom? (Take \( g = 10 \, \text{m/s}^2 \))

Potential energy \( mgh = 6 \times 10 \times 10 = 600 \, \text{J} \).

Kinetic energy \( \frac{1}{2} m v^2 = 600 \Rightarrow v^2 = 200 \Rightarrow v = \sqrt{200} \approx 14.14 \, \text{m/s} \).

13.5 m/s
14 m/s
14.5 m/s
15 m/s
2

A neutron (\( 1 \, \text{u} \)) moving at \( 2 \times 10^6 \, \text{m/s} \) collides elastically with a carbon nucleus (\( 12 \, \text{u} \)). What fraction of its kinetic energy is retained?

Fraction retained \( f_1 = \left( \frac{m_1 - m_2}{m_1 + m_2} \right)^2 = \left( \frac{1 - 12}{1 + 12} \right)^2 = \left( \frac{-11}{13} \right)^2 = \frac{121}{169} \approx 0.716 \).

0.65
0.72
0.78
0.85
2

A \( 8 \, \text{kg} \) mass falls from \( 5 \, \text{m} \) onto a spring (\( k = 2500 \, \text{N/m} \)). What is the maximum compression? (Take \( g = 10 \, \text{m/s}^2 \))

Potential energy \( mgh = 8 \times 10 \times 5 = 400 \, \text{J} \).

Spring energy \( \frac{1}{2} k x_m^2 = 400 \Rightarrow 1250 x_m^2 = 400 \Rightarrow x_m = \sqrt{0.32} \approx 0.566 \, \text{m} \).

0.5 m
0.57 m
0.6 m
0.65 m
2

A force \( F = 10x^2 \, \text{N} \) acts from \( x = 0 \) to \( x = 1 \, \text{m} \). What is the work done?

Work \( W = \int_0^1 10x^2 \, dx = \left[ \frac{10}{3} x^3 \right]_0^1 = \frac{10}{3} \times 1 = \frac{10}{3} \approx 3.33 \, \text{J} \).

3 J
3.3 J
3.6 J
4 J
2

A spring with constant \( k = 200 \, \text{N/m} \) is compressed by \( 0.1 \, \text{m} \). What is the potential energy stored in the spring?

Potential energy \( V = \frac{1}{2} k x^2 \).

\( V = \frac{1}{2} \times 200 \times (0.1)^2 = 100 \times 0.01 = 1 \, \text{J} \).

0.5 J
1 J
1.5 J
2 J
2

A motor lifts a \( 2000 \, \text{kg} \) load at \( 2.5 \, \text{m/s} \) against \( 6000 \, \text{N} \) friction. What is the power? (Take \( g = 10 \, \text{m/s}^2 \))

Force \( F = mg + F_f = 2000 \times 10 + 6000 = 26000 \, \text{N} \).

Power \( P = F \cdot v = 26000 \times 2.5 = 65000 \, \text{W} \).

63 kW
65 kW
67 kW
69 kW
2

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