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.
\(\dfrac{4}{5} \times 30~\text{N}\)
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| 1. | \(\dfrac g 3\) to left, \(g\) upward, \(g\) downward. |
| 2. | zero, zero, \(g\) downward. |
| 3. | zero, \(g\) upward, \(g\) downward. |
| 4. | \(g\) to right, zero, \(g\) downward. |
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| 1. | \(\dfrac{3 g}{5} ~\text{down}\). | 2. | \(\dfrac{6 g}{5}\text{ down}\). |
| 3. | \(\dfrac{g}{5}\text{ down}\). | 4. | \(\dfrac{11 g}{5}\text{ down}\). |
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1. to the right.
2. to the left.
3. upward.
4. downward.
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| 1. | \(k_1x-k_2x=ma \) |
| 2. | \(\dfrac{k_1k_2}{k_1+k_2}x=ma \) |
| 3. | \(k_1x+k_2x=ma \) |
| 4. | \(\dfrac{k_1k_2}{k_1-k_2}=ma \) |
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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)
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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. |
2. Only Q is True.
3. P, Q are True.
4. Only R is True.
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| 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. | \(m^2E_m=M^2E_M\) |
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1. \(g\)
2. \(g~\text{sin}30^{\circ}\)
3. \(g~\text{cos}30^{\circ}\)
4. \(g~\text{tan}30^{\circ}\)
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The relative acceleration of the blocks has the magnitude:
1. \(\dfrac{g}{5}\)
2. \(\dfrac{2g}{5}\)
3. \(\dfrac{3g}{5}\)
4. \(\dfrac{4g}{5}\)
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