The angle between \(\mathrm{A}=\hat{\mathbf{i}}+\hat{\mathbf{j}}\) and \(\mathrm{B}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\) is:
1. \(45^{\circ} \)
2. \(90^{\circ} \)
3. \(-45^{\circ} \)
4. \(180^{\circ}\)
Subtopic:  Scalar Product |
 78%
From NCERT
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If a vector \(2\hat{i}+3\hat{j}+8\hat{k}\) is perpendicular to the vector \(-4\hat{i}+4\hat{j}+\alpha \hat{k},\) then the value of \(\alpha\) will be:
1. -1
2. -12
3. 12
4. \(1\)

Subtopic:  Scalar Product |
 60%
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A block of \(1\) kg is released from a top of a smooth curve AB, and then it encounters a rough surface BC, coming to rest at C. The work done by friction is: (\(g=10\) m/s2)
           
1. \(25\) J
2. \(50\) J
3. \(-25\) J
4. \(-50\) J

Subtopic:  Work Energy Theorem |
 69%
From NCERT
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The work done by all the forces (external and internal) on a system equals the change in:

1. total energy 2. kinetic energy
3. potential energy 4. none of these
Subtopic:  Work Energy Theorem |
 73%
From NCERT
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A bullet from a gun is fired on a rectangular wooden block with velocity \(u\). When bullet travels \(24\) cm through the block along its length horizontally, velocity of bullet becomes \(u/3\). Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:
1. \(30\) cm
2. \(27\) cm
3. \(24\) cm
4. \(28\) cm
Subtopic:  Work Energy Theorem |
 65%
From NCERT
NEET - 2023
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A body of mass \(1\) kg is thrown upwards with a velocity \(20\) ms-1. It momentarily comes to rest after attaining a height of \(18\) m. How much energy is lost due to air friction?
(Take \(g=10\) ms-2)
1. \(20\) J
2. \(30\) J
3. \(40\) J
4. \(10\) J

Subtopic:  Work Energy Theorem |
 87%
From NCERT
AIPMT - 2009
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A bicyclist comes to a skidding stop in \(10\) m. During this process, the force on the bicycle due to the road is \(200\) N is directly opposed to the motion. The work done by the cycle on the road is:
1. \(+2000\) J
2. \(-200\) J
3. zero
4. \(-20000\) J

Subtopic:  Work done by constant force |
 58%
From NCERT
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The work done by gravity on a projectile of mass \(m\) fired with a speed \(u\) at an angle \(\theta\) to the horizontal, until the time of impact is:
          
1. zero 2. \(-\frac12mu^2cos^2\theta\)
3. \(-\frac12mu^2sin^2\theta\) 4. \(-\frac12mu^2\)
Subtopic:  Work done by constant force |
 59%
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A force of \(100\) N acts on a block, always acting opposite to its velocity. The block moves from \(x=4\) m to \(x=10\) m and then to \(x=6\) m. The work done by the force is:
1.  \(200\) J
2.  \(-200\) J
3.  \(1000\) J
4.  \(-1000\) J
Subtopic:  Work done by constant force |
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A body of mass \(0.5\) kg travels in a straight line with velocity \(v=ax^{3/2}\) where \(a=5~\mathrm{m^{-1/2}s^{-1}}\). The work done by the net force during its displacement from \(x=0\) m to \(x=2\) m is:
1. \(15\) J
2. \(50\) J
3. \(10\) J
4. \(100\) J

Subtopic:  Work Done by Variable Force |
 66%
From NCERT
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