Work Energy and Power Chapter-Wise Test 2

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A force \( F = 8x \, \text{N} \) acts from \( x = 0 \) to \( x = 2 \, \text{m} \). What is the work done?

Work \( W = \int_0^2 8x \, dx = \left[ 4x^2 \right]_0^2 = 4 \times 4 = 16 \, \text{J} \).

14 J
16 J
18 J
20 J
2

A force \( \mathbf{F} = 7\hat{\mathbf{i}} - 3\hat{\mathbf{j}} \, \text{N} \) acts on a particle moving along \( \mathbf{d} = 2\hat{\mathbf{i}} + 6\hat{\mathbf{j}} \, \text{m} \). What is the work done?

Work \( W = \mathbf{F} \cdot \mathbf{d} \).

\( \mathbf{F} = 7\hat{\mathbf{i}} - 3\hat{\mathbf{j}} \), \( \mathbf{d} = 2\hat{\mathbf{i}} + 6\hat{\mathbf{j}} \).

Scalar product: \( W = (7 \times 2) + (-3 \times 6) = 14 - 18 = -4 \, \text{J} \).

-6 J
-4 J
-2 J
0 J
2

A spring (\( k = 450 \, \text{N/m} \)) is compressed by \( 0.15 \, \text{m} \). What is the stored potential energy?

Potential energy \( V = \frac{1}{2} k x^2 = \frac{1}{2} \times 450 \times (0.15)^2 = 225 \times 0.0225 = 5.0625 \, \text{J} \approx 5.06 \, \text{J} \).

4.8 J
5.1 J
5.3 J
5.5 J
2

A force \( F = 2x \, \text{N} \) acts on a particle from \( x = 1 \, \text{m} \) to \( x = 3 \, \text{m} \). What is the work done?

Work \( W = \int_1^3 2x \, dx = \left[ x^2 \right]_1^3 = 9 - 1 = 8 \, \text{J} \).

6 J
8 J
10 J
12 J
2

A \( 7 \, \text{kg} \) mass at \( 14 \, \text{m/s} \) 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
4 m/s
7 m/s
10 m/s
1

A \( 7 \, \text{kg} \) block is pushed with \( 35 \, \text{N} \) over \( 10 \, \text{m} \) on a frictionless surface, starting from rest. What is its final speed?

Work \( W = 35 \times 10 = 350 \, \text{J} \).

By work-energy theorem, \( K_f = W \Rightarrow \frac{1}{2} \times 7 \times v^2 = 350 \Rightarrow v^2 = 100 \Rightarrow v = 10 \, \text{m/s} \).

9 m/s
10 m/s
11 m/s
12 m/s
2

A bullet of mass \( 20 \, \text{g} \) with speed \( 300 \, \text{m/s} \) passes through a wooden block and emerges with \( 20\% \) of its initial kinetic energy. What is the emergent speed?

Initial \( K = \frac{1}{2} \times 0.02 \times 300^2 = 900 \, \text{J} \).

Final \( K = 0.2 \times 900 = 180 \, \text{J} \).

\( \frac{1}{2} \times 0.02 \times v_f^2 = 180 \Rightarrow v_f^2 = 18000 \Rightarrow v_f = \sqrt{18000} \approx 134.2 \, \text{m/s} \).

120 m/s
134 m/s
150 m/s
160 m/s
2

A \( 9 \, \text{kg} \) mass falls from \( 6 \, \text{m} \) onto a spring (\( k = 3000 \, \text{N/m} \)). What is the maximum compression? (Take \( g = 10 \, \text{m/s}^2 \))

Potential energy \( mgh = 9 \times 10 \times 6 = 540 \, \text{J} \).

Spring energy \( \frac{1}{2} k x_m^2 = 540 \Rightarrow 1500 x_m^2 = 540 \Rightarrow x_m = \sqrt{0.36} = 0.6 \, \text{m} \).

0.55 m
0.6 m
0.65 m
0.7 m
2

A \( 5 \, \text{kg} \) block is pushed with \( 25 \, \text{N} \) over \( 8 \, \text{m} \) on a frictionless surface, starting from \( 1 \, \text{m/s} \). What is its final speed?

Initial \( K_i = \frac{1}{2} \times 5 \times 1^2 = 2.5 \, \text{J} \).

Work \( W = 25 \times 8 = 200 \, \text{J} \).

Final \( K_f = K_i + W = 2.5 + 200 = 202.5 \, \text{J} \Rightarrow v_f = \sqrt{\frac{2 \times 202.5}{5}} = \sqrt{81} = 9 \, \text{m/s} \).

8 m/s
9 m/s
10 m/s
11 m/s
2

A \( 1.8 \, \text{kg} \) object is dropped from \( 18 \, \text{m} \). What is its kinetic energy just before hitting the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Potential energy \( V = mgh = 1.8 \times 10 \times 18 = 324 \, \text{J} \).

By conservation, \( K_f = V_i = 324 \, \text{J} \).

300 J
324 J
340 J
360 J
2

A \( 1200 \, \text{kg} \) car moving at \( 15 \, \text{m/s} \) compresses a spring (\( k = 8 \times 10^3 \, \text{N/m} \)). What is the maximum compression?

Initial \( K = \frac{1}{2} \times 1200 \times 15^2 = 135000 \, \text{J} \).

Spring energy \( \frac{1}{2} k x_m^2 = 135000 \Rightarrow 4000 x_m^2 = 135000 \Rightarrow x_m = \sqrt{33.75} \approx 5.81 \, \text{m} \).

5.5 m
5.8 m
6 m
6.2 m
2

A \( 2 \, \text{kg} \) block slides down a frictionless incline from \( 9 \, \text{m} \) height. What is its speed at the bottom? (Take \( g = 10 \, \text{m/s}^2 \))

Potential energy \( mgh = 2 \times 10 \times 9 = 180 \, \text{J} \).

Kinetic energy \( \frac{1}{2} m v^2 = 180 \Rightarrow v^2 = 180 \Rightarrow v = \sqrt{180} \approx 13.42 \, \text{m/s} \).

12 m/s
13 m/s
13.4 m/s
14 m/s
3

A \( 3.5 \, \text{kg} \) mass falls from \( 7 \, \text{m} \) onto a spring (\( k = 1200 \, \text{N/m} \)). What is the maximum compression? (Take \( g = 10 \, \text{m/s}^2 \))

Potential energy \( mgh = 3.5 \times 10 \times 7 = 245 \, \text{J} \).

Spring energy \( \frac{1}{2} k x_m^2 = 245 \Rightarrow 600 x_m^2 = 245 \Rightarrow x_m = \sqrt{0.4083} \approx 0.639 \, \text{m} \).

0.6 m
0.64 m
0.7 m
0.75 m
2

A spring (\( k = 900 \, \text{N/m} \)) is compressed from \( 0.15 \, \text{m} \) to \( 0.25 \, \text{m} \). What is the work done by the spring force?

Work \( W_s = \frac{1}{2} k (x_i^2 - x_f^2) = \frac{1}{2} \times 900 \times (0.15^2 - 0.25^2) = 450 \times (0.0225 - 0.0625) = -18 \, \text{J} \).

-20 J
-18 J
-16 J
-14 J
2

A \( 2.5 \, \text{kg} \) 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 \( mgh = 2.5 \times 10 \times 10 = 250 \, \text{J} \).

Kinetic energy \( \frac{1}{2} m v^2 = 250 \Rightarrow v^2 = 200 \Rightarrow v = \sqrt{200} \approx 14.14 \, \text{m/s} \).

13 m/s
14 m/s
14.5 m/s
15 m/s
2

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