Q. No.A force \(F=x^2 y \hat{\imath}+y^2 \hat{\jmath} \) acts on a particle in a plane \(x+y=10.\) The work done by this force during a displacement from \((0,0)\) to \((4~\text m,2~\text m)\) is: (round off to the nearest integer)
1. \(110~\text J\)
2. \(227~\text J\)
3. \(152~\text J\)
4. \(375~\text J\)
1. \(110~\text J\)
2. \(227~\text J\)
3. \(152~\text J\)
4. \(375~\text J\)
Subtopic: Work Done by Variable Force |
77%
Level 2: 60%+
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A force \(F = \alpha + \beta x^2 \) acts on an object in the \(x-\)direction. The work done by the force is \(5~\text J\) when the object is displaced by \(1~\text m.\) If the constant \(a= 1~\text N\) then \(\beta\) will be:
1. \(12 ~\text {N/m}^2\)
2. \(10 ~\text {N/m}^2\)
3. \(15 ~\text {N/m}^2\)
4. \(8~\text {N/m}^2\)
1. \(12 ~\text {N/m}^2\)
2. \(10 ~\text {N/m}^2\)
3. \(15 ~\text {N/m}^2\)
4. \(8~\text {N/m}^2\)
Subtopic: Work Done by Variable Force |
88%
Level 1: 80%+
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A force \(\left(3 x^2+2 x-5\right)~\text N\) displaces a body from \(x = 2~\text m\) to \(x = 4~\text m.\) Work done by this force is: ________ J.
1. \(64~\text J\)
2. \(36~\text J\)
3. \(58~\text J\)
4. \(87~\text J\)
1. \(64~\text J\)
2. \(36~\text J\)
3. \(58~\text J\)
4. \(87~\text J\)
Subtopic: Work Done by Variable Force |
92%
Level 1: 80%+
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A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation \(\begin{equation} v=\alpha \sqrt{x} \end{equation}\), where \(\begin{equation} \alpha \end{equation}\) is a constant. The total work done by all the forces applied on the particle during its displacement from \(x=0\) to \(x=d\), will be :
1. \(\begin{equation} \frac{m}{2 \alpha^2 d} \end{equation}\)
2. \(\begin{equation} \frac{m d}{2 \alpha^2} \end{equation}\)
3. \(\begin{equation} \frac{m \alpha^2 d}{2} \end{equation}\)
4. \(\begin{equation} 2 m \alpha^2 d \end{equation}\)
1. \(\begin{equation} \frac{m}{2 \alpha^2 d} \end{equation}\)
2. \(\begin{equation} \frac{m d}{2 \alpha^2} \end{equation}\)
3. \(\begin{equation} \frac{m \alpha^2 d}{2} \end{equation}\)
4. \(\begin{equation} 2 m \alpha^2 d \end{equation}\)
Subtopic: Work Done by Variable Force |
86%
Level 1: 80%+
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A variable force given by; \(F=5kx \) (in newtons) acts on a body moving along the \(x\)-axis, where \(k\) is a constant.
What is the work done by this force as the body moves from \(x=2~\text{m}\) to \(x=5~\text{m}\)?
What is the work done by this force as the body moves from \(x=2~\text{m}\) to \(x=5~\text{m}\)?
| 1. | \(\left ( \dfrac{205}{2}k \right )\text{J} \) | 2. | \(\left ( \dfrac{105}{2}k \right )\text{J} \) |
| 3. | \((52k)~\text{J}\) | 4. | \((51k)~\text{J}\) |
Subtopic: Work Done by Variable Force |
78%
Level 2: 60%+
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A particle is constrained to move along the \(x \text-\)axis under the action of a force:
\(\overrightarrow{F}=(2+3 x) \hat{i}.\)
What is the work done by this force when the particle is displaced from \(x = 0\) to \(x = 4 ~\text{m}\text{?}\)
1. \(16 \) J
2. \(32 \) J
3. \(4 \) J
4. \(8 \) J
Subtopic: Work Done by Variable Force |
87%
Level 1: 80%+
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If a force \(F \) applied on an object moving along the \(y\)-axis varies with the \(y\)-coordinate as \(F=3+2y^{2}. \) The work done in displacing the body from \(y=2\text{ m}\) to \(y=5\text{ m}\) is:
1. \(87\text{ J}\)
2. \(0 \)
3. \(57\text{ J}\)
4. \(72\text{ J}\)
1. \(87\text{ J}\)
2. \(0 \)
3. \(57\text{ J}\)
4. \(72\text{ J}\)
Subtopic: Work Done by Variable Force |
84%
Level 1: 80%+
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Arrange the four graphs in descending order of total work done; where \(W_1, W_2, W_3 ~\text{and}~W_4\) are the work done corresponding to figures \(a,b,c~\text{and}~d\) respectively.
| 1. | \( W_3>W_2>W_1>W_4 \) |
| 2. | \( W_3>W_2>W_4>W_1 \) |
| 3. | \({W}_2>{W}_3>{W}_4>{W}_1 \) |
| 4. | \(W_2>W_3>W_1>W_4\) |
Subtopic: Work Done by Variable Force |
68%
Level 2: 60%+
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A particle of mass \(500\) g is moving in a straight line with velocity \(v=b x^{5 / 2}\). The work done by the net force during its displacement from \(x = 0\) to \(x=4\) m is:
(Take \(b=0.25\) m–3/2 s–1)
(Take \(b=0.25\) m–3/2 s–1)
| 1. | \(2\) J | 2. | \(4\) J |
| 3. | \(8\) J | 4. | \(16\) J |
Subtopic: Work Done by Variable Force |
64%
Level 2: 60%+
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A force of \(F=(5y+20)\hat{j}~\text{N}\) acts on a particle. The work done by this force when the particle is moved from \(y=0~\text{m}\) to \(y=10~\text{m}\) is:
1. \(150~\text J\)
2. \(270~\text J\)
3. \(450~\text J\)
4. \(580~\text J\)
1. \(150~\text J\)
2. \(270~\text J\)
3. \(450~\text J\)
4. \(580~\text J\)
Subtopic: Work Done by Variable Force |
80%
Level 1: 80%+
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