- 1(current)
Q. No.
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A body of mass \(0.5~\text{kg}\) travels in a straight line with velocity \(v=ax^{(3/2)}\) where \(a=5~\text{m}^{-1/2}\text{s}^{-1}\). The work done by the net force during its displacement from \(x=0~\text{m}\) to \(x=2~\text{m}\) is:
1. \(15~\text{J}\)
2. \(50~\text{J}\)
3. \(10~\text{J}\)
4. \(100~\text{J}\)
Subtopic: Â Work Done by Variable Force |
 68%
Level 2: 60%+
Hints
A horizontal force \(F\) acts on a \(2~\text{kg}\) block placed on a smooth horizontal plane. It varies with time \(t\) as shown in the figure. The block is initially at rest.
The work done by the force until \(t=2~\text s,\) equals:
1. \(6.25 ~\text J\)
2. \(4.5 ~\text J\)
3. \(2.25 ~\text J\)
4. \(1.5~\text J\)
The work done by the force until \(t=2~\text s,\) equals:
1. \(6.25 ~\text J\)
2. \(4.5 ~\text J\)
3. \(2.25 ~\text J\)
4. \(1.5~\text J\)
Subtopic: Â Work Done by Variable Force |
 64%
Level 2: 60%+
Hints
The work done by a force \(F=2x^2\) (newton) in a displacement from \(x=0\) (origin) to \(x=3\) m is:
1. \(54\) J
2. \(27\) J
3. \(18\) J
4. \(9\) J
1. \(54\) J
2. \(27\) J
3. \(18\) J
4. \(9\) J
Subtopic: Â Work Done by Variable Force |
 84%
Level 1: 80%+
Hints
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A block is moved along a horizontal plane by means of a force of constant magnitude of \(5\) N, but acting at an angle \(\theta\) which is proportional to the displacement (\(x\)): \(\theta=\dfrac{1}{2} x, \) where \(x\) is in \(\text{m}\) and \(\theta\) is in radians. The work done by this force until the force becomes vertical is:
1. \(5\text{ J}\)
2. \(10 \text{ J}\)
3. \(2.5\text{ J}\)
4. \(1.25\text{ J}\)
1. \(5\text{ J}\)
2. \(10 \text{ J}\)
3. \(2.5\text{ J}\)
4. \(1.25\text{ J}\)
Subtopic: Â Work Done by Variable Force |
Level 3: 35%-60%
Hints
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A block of mass \(m\) moving with a speed \(v\) meets an unextended spring fixed at one end, and having a spring constant \(k.\) During maximum compression, the mid-point of the spring undergoes a rightward displacement \(x\). Then, \(v=\)
| 1. | \(\sqrt{\dfrac{k}{m}}x\) | 2. | \(\sqrt{\dfrac{m}{k}}x\) |
| 3. | \(\sqrt{\dfrac{k}{m}}(2x)\) | 4. | \(\sqrt{\dfrac{k}{m}}\left(\dfrac{x}{2}\right)\) |
Subtopic: Â Work Done by Variable Force |
Level 3: 35%-60%
Hints
- 1(current)
Q. No.
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