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Q. No.A mass of \(6~\text{kg}\) is suspended by a rope of negligible mass and a length of \(2~\text{m}\) from the ceiling. A force of \(60~\text{N}\) in the horizontal direction is applied at the mid-point \(P\) of the rope (see figure). The angle the rope makes with the vertical in equilibrium is:
(take \(g=10~\text{ms}^{-2}\))
1. \(15^\circ\)
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)
Subtopic: Tension & Normal Reaction |
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A curve in a level road has a radius of \(75\) m. The maximum speed of a car turning this curved road can be \(30\) m/s without skidding. If the radius of the curved road is changed to \(48\) m and the coefficient of friction between the tyres and the road remains the same, then the maximum allowed speed would be:
1. \(12\) m/s
2. \(24\) m/s
3. \(32\) m/s
4. \(44\) m/s
1. \(12\) m/s
2. \(24\) m/s
3. \(32\) m/s
4. \(44\) m/s
Subtopic: Banking of Roads |
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A person is standing in an elevator. In which situation does he experience weight loss?
| 1. | When the elevator moves upward with constant acceleration. |
| 2. | When the elevator moves downward with constant acceleration. |
| 3. | When the elevator moves upward with uniform velocity. |
| 4. | When the elevator moves downward with uniform velocity. |
Subtopic: Application of Laws |
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In the arrangement shown in figure \(a_1,a_2,a_3\text{ and } a_4\) are the accelerations of masses \(m_1,m_2,m_3\text{ and }m_4\) respectively. Which of the following relation is true for this arrangement?
1. \(4 a_1+2 a_2+a_3+a_4=0 \)
2. \(a_1+4 a_2+3 a_3+a_4=0 \)
3. \( \mathrm{a}_1+4 \mathrm{a}_2+3 \mathrm{a}_3+2 \mathrm{a}_4=0 \)
4. \( 2 a_1+2 a_2+3 a_3+a_4=0\)
1. \(4 a_1+2 a_2+a_3+a_4=0 \)
2. \(a_1+4 a_2+3 a_3+a_4=0 \)
3. \( \mathrm{a}_1+4 \mathrm{a}_2+3 \mathrm{a}_3+2 \mathrm{a}_4=0 \)
4. \( 2 a_1+2 a_2+3 a_3+a_4=0\)
Subtopic: String Constraint |
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A batsman hits back a ball of mass \(0.4\text{ kg}\) straight in the direction of the bowler without changing its initial speed of \(15\text{ m/s}.\) The impulse imparted to the ball is:
1. \(10\text{ Ns}\)
2. \(11\text{ Ns}\)
3. \(12\text{ Ns}\)
4. \(13\text{ Ns}\)
1. \(10\text{ Ns}\)
2. \(11\text{ Ns}\)
3. \(12\text{ Ns}\)
4. \(13\text{ Ns}\)
Subtopic: Newton's Laws |
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A mass \(M\) is suspended by a light string from a rigid support. A force \(F\) is acting on the string as shown in the figure and the string makes an angle \(\theta\) with the vertical.
Which of the following expressions is correct?
1. \(T\cos\theta =F\)
2. \(T\sin\theta =Mg \)
3. \(F=Mg\tan\theta \)
4. \(F=\tan\theta \)
Which of the following expressions is correct?
1. \(T\cos\theta =F\)
2. \(T\sin\theta =Mg \)
3. \(F=Mg\tan\theta \)
4. \(F=\tan\theta \)
Subtopic: Tension & Normal Reaction |
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A \(1500\) kg automobile collides with a wall in a particular crash test. The automobile's initial velocity is \(v_1=15\) m/s, and its final velocity in the opposite direction is \(v_2=2.6\) m/s. If the collision lasts for \(0.15\) s, then the average force exerted on the automobile is:
| 1. | \(2.6\times 10^4~\text{N}\) | 2. | \(2.25\times 10^4~\text{N}\) |
| 3. | \(1.76\times 10^5~\text{N}\) | 4. | \(3.9\times 10^3~\text{N}\) |
Subtopic: Newton's Laws |
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A \(2~\text{kg}\) box is resting on a horizontal floor. A horizontal force of \(30~\text{N}\) is applied to the box, but it does not move. The coefficient of static friction is: (take \(g=10~\text{m/s}^2\))
| 1. | \(\dfrac{2}{3}\) | 2. | \(\dfrac{3}{2}\) |
| 3. | \(\dfrac{1}{2}\) | 4. | \(\dfrac{1}{3}\) |
Subtopic: Friction |
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A stone of mass m, tied to a string, is being whirled in a vertical circle with a uniform speed. The tension in the string is:
| 1. | the same throughout the motion |
| 2. | minimum at the highest position of the circular path |
| 3. | minimum at the lowest position of the circular path |
| 4. | minimum when the rope is in the horizontal position |
Subtopic: Uniform Circular Motion |
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A block of mass \(10\text{ kg}\) starts sliding on a surface with an initial velocity of \(9.8\text{ m/s}.\) The coefficient of friction between the surface and block is \(0.5.\) The distance covered by the block before coming to rest is: [use \(g = 9.8\text{ m/s}^2\)]
1. \(4.9\text{ m}\)
2. \(9.8\text{ m}\)
3. \(12.5\text{ m}\)
4. \(19.6\text{ m}\)
1. \(4.9\text{ m}\)
2. \(9.8\text{ m}\)
3. \(12.5\text{ m}\)
4. \(19.6\text{ m}\)
Subtopic: Friction |
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