Q. No.The average force needed to accelerate a car weighing \(500~\text{kg}\) from rest to \(36~\text{km/h}\) through a distance of \(25~\text{m}\), up a \(30^{\circ}\) incline is \((g =10~\text{m/s}^2)\):
1. \(1000~\text{N}\)
2. \(2500~\text{N}\)
3. \(1500~\text{N}\)
4. \(3500~\text{N}\)
1. \(1000~\text{N}\)
2. \(2500~\text{N}\)
3. \(1500~\text{N}\)
4. \(3500~\text{N}\)
Subtopic: Application of Laws |
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A ball of mass \(m\) falls from a height \(h\) onto the ground and rebounds to a height \(\dfrac{h}{4}\). The impulse on the ball from the ground has the magnitude:
| 1. | \(\dfrac{3}{4}m\sqrt{2gh}\) |
| 2. | \(\dfrac{5}{4}m\sqrt{2gh}\) |
| 3. | \(\dfrac{3}{2}m\sqrt{2gh}\) |
| 4. | \(\dfrac{1}{2}m\sqrt{2gh}\) |
Subtopic: Application of Laws |
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A wire connects two blocks of masses \(M\), \(2M\); both lying on a smooth horizontal plane.
When a force \(F_1\) is applied to \(2M\) as shown in figure 1, the wire just breaks. On the other hand, when \(F_2\) is applied to \(M\) as shown in figure 2,
the wire just breaks. Assume that the mass of the wire is negligible. Then:
| 1. | \(F_1 =F_2\) |
| 2. | \(F_1>F_2\) |
| 3. | \(F_1<F_2\) |
| 4. | Any of the above is possible |
Subtopic: Application of Laws |
55%
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The acceleration of the \(4\) kg block is:
| 1. | \(\dfrac{3 g}{5} ~\text{down}\). | 2. | \(\dfrac{6 g}{5}\text{ down}\). |
| 3. | \(\dfrac{g}{5}\text{ down}\). | 4. | \(\dfrac{11 g}{5}\text{ down}\). |
Subtopic: Application of Laws |
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A uniform rod is pivoted at one of its ends, so that it can rotate freely in a vertical plane. Initially, it hangs vertically as shown in the figure. A sharp impulse is delivered to the rod at its lowest end \(B,\) towards the right. An impulse is exerted by the pivot at \(A,\) due to the constraint. The impulse at \(A\) acts:
1. to the right.
2. to the left.
3. upward.
4. downward.
1. to the right.
2. to the left.
3. upward.
4. downward.
Subtopic: Application of Laws |
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A small block of mass \(m\) is released as shown in the figure against the vertical part of the smooth curved surface of a wedge of mass \(M\), initially at rest. When the block reaches the bottom, it travels horizontally with a kinetic energy \(E_m,\) while the wedge recoils towards left with a kinetic energy \(E_M.\) Then:
| 1. | \(\dfrac{E_m}{m}=\dfrac{E_M}{M}\) | 2. | \(mE_m=ME_M\) |
| 3. | \(\dfrac{E_m}{m^2}=\dfrac{E_M}{M^2}\) | 4. | \(m^2E_m=M^2E_M\) |
Subtopic: Application of Laws |
67%
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A box is moving down a frictionless \(30^{\circ}\) incline, and a particle is projected within the box. The acceleration of the particle relative to the box is:
1. \(g\)
2. \(g~\text{sin}30^{\circ}\)
3. \(g~\text{cos}30^{\circ}\)
4. \(g~\text{tan}30^{\circ}\)
1. \(g\)
2. \(g~\text{sin}30^{\circ}\)
3. \(g~\text{cos}30^{\circ}\)
4. \(g~\text{tan}30^{\circ}\)
Subtopic: Application of Laws |
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The two blocks \(A,B\) have identical masses and are placed on a smooth horizontal plane. The pulley \(P\) is light, and is rigidly connected to the block \(A\) by means of a horizontal light rod. The string connecting block \(B\) is also horizontal. A force \(F\) is acting vertically on the string, and the two blocks move horizontally. The force on \(A\) due to rod is:
1. \(F\)
2. \(2F\)
3. \(\sqrt2F\)
4. \(\dfrac{F}{\sqrt2}\)
1. \(F\)
2. \(2F\)
3. \(\sqrt2F\)
4. \(\dfrac{F}{\sqrt2}\)
Subtopic: Application of Laws |
55%
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The two blocks \(A,B\) have identical masses and are connected by an ideal string. The block \(B\) lies on a smooth horizontal table with the connecting string horizontal and passing over a smooth light pulley. The relative acceleration of \(A\) with respect to \(B\) is:
1. \(g\)
2. \(\dfrac{g}{2}\)
3. \(\dfrac{g}{\sqrt2}\)
4. \(g\sqrt2\)
1. \(g\)
2. \(\dfrac{g}{2}\)
3. \(\dfrac{g}{\sqrt2}\)
4. \(g\sqrt2\)
Subtopic: Application of Laws |
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In the system shown in the figure, the strings and pulleys are ideal, and the block \(A\) moves downward while \(B\) moves to the right. \(A, B \) have equal masses. The acceleration of the block \(B\) is:
| 1. | \(\dfrac{g}{2}\) | 2. | \(\dfrac{g}{5}\) |
| 3. | \(\dfrac{2g}{5}\) | 4. | \(g\) |
Subtopic: Application of Laws |
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