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Q. No.A \(3\) kg-block is pressed against a vertical wall with a coefficient of friction, \(\mu = \dfrac{3}{4}\). What minimum force should be applied to the block in order to prevent it from falling down? Take \(g = 10 ~\text{m/s}^2\)
1.
\(\dfrac{3}{4} \times 30 ~\text{N}\)
2.
\(\dfrac{4}{3} \times 30 ~\text{N}\)
3.
\(\dfrac{3}{5} \times 30 ~\text{N}\)
4.
\(\dfrac{4}{5} \times 30~\text{N}\)
| 1. | \(\dfrac{3}{4} \times 30 ~\text{N}\) | 2. | \(\dfrac{4}{3} \times 30 ~\text{N}\) |
| 3. | \(\dfrac{3}{5} \times 30 ~\text{N}\) | 4. | \(\dfrac{4}{5} \times 30~\text{N}\) |
Subtopic: Friction |
Level 4: Below 35%
Hints
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 |
Level 4: Below 35%
Hints
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 |
Level 3: 35%-60%
Hints
The two blocks \(A,~B\) are connected by an inextensible string, and are lying on a horizontal surface. The blocks move under the action of forces of magnitudes \(F_1\) and \(F_2,\) as shown in the figure. The surface exerts non-zero frictional forces \(f_A,~f_B\) (towards right).
Consider the following situations:
Which of the above, are possible? Assume that the string is taut.
1. (P) or (Q)
2. (R) or (S)
3. Any of (P), (Q), (R), (S)
4. Only (P)
Consider the following situations:
| (P) | \(f_A,~f_B>0\) | (Q) | \(f_A,~f_B<0\) |
| (R) | \(f_A>0,~ f_B<0\) | (S) | \(f_A<0,~ f_B>0\) |
Which of the above, are possible? Assume that the string is taut.
1. (P) or (Q)
2. (R) or (S)
3. Any of (P), (Q), (R), (S)
4. Only (P)
Subtopic: Friction |
Level 3: 35%-60%
Hints
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A block of mass \(m\) is placed on a flat horizontal surface, and the coefficient of friction between the block and the surface is \(\mu\). A force \(F_A\) is applied to the block from above, and a force \(F_R\) is applied to the right. In all situations being considered below, the block remains at rest. Let \(f\) be the force of friction on the block.
Consider the statements:
Choose the correct option from the given ones:
Consider the statements:
| (P) | \(f\) increases if \(m\) is increased. |
| (Q) | \(f\) increases if \(F_A\) is increased. |
| (R) | \(f\) increases if \(F_R\) is increased. |
Choose the correct option from the given ones:
| 1. | Only (P) is true. | 2. | Only (Q) is true. |
| 3. | (P) and (Q) are true. | 4. | Only (R) is true. |
Subtopic: Friction |
Level 3: 35%-60%
Hints
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 |
Level 3: 35%-60%
Hints
An Atwood's machine with blocks of masses \(3\) kg and \(2\) kg is set up in a laboratory. The string is taut and the blocks start moving at \(t=0.\)
The relative acceleration of the blocks has the magnitude:
1. \(\dfrac{g}{5}\)
2. \(\dfrac{2g}{5}\)
3. \(\dfrac{3g}{5}\)
4. \(\dfrac{4g}{5}\)
The relative acceleration of the blocks has the magnitude:
1. \(\dfrac{g}{5}\)
2. \(\dfrac{2g}{5}\)
3. \(\dfrac{3g}{5}\)
4. \(\dfrac{4g}{5}\)
Subtopic: Application of Laws |
52%
Level 3: 35%-60%
Hints
A balloon ascending with an acceleration \(a\) has a ballast of mass \(m\) thrown out, and it is observed to move upward with double the acceleration. The mass of the remaining part (after the ballast is thrown out) is:
| 1. | \(m\dfrac{g+2a}{g+a}\) |
| 2. | \(m\dfrac{g+a}{g}\) |
| 3. | \(m\dfrac{g+a}{a}\) |
| 4. | \(m\dfrac{g+2a}{g}\) |
Subtopic: Newton's Laws |
50%
Level 3: 35%-60%
Hints
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 |
Level 3: 35%-60%
Hints
A \(2\) kg brick is placed on the ground as shown and it is symmetrically cut into two equal pieces by a plane \(AB,\) which is at \(45^{\circ}\) with the horizontal. The system remains at rest. The force of friction on the upper piece due to the lower is: (Take \(g\) = \(10\) m/s2)
1. \(10\) N
2. \(10 \sqrt 2\) N
3. \(5 \sqrt 2\) N
4. \(5\) N
1. \(10\) N
2. \(10 \sqrt 2\) N
3. \(5 \sqrt 2\) N
4. \(5\) N
Subtopic: Friction |
57%
Level 3: 35%-60%
Hints
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