Q. No.A body of mass \(m\) is slipping on a rough horizontal plane, decelerating at \(6\) m/s2. The net force exerted by the plane on the body is: (take \(g =10~\text{m/s}^{2}\))
1. \(1.6~mg\)
2. \(0.4~mg\)
3. \(\sqrt{1.36}~mg\)
4. \(\sqrt{1.16}~mg\)
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| Column-I | Column-II | ||
| \(\mathrm{(A)}\) | \(F_{\text{ext}}=mg,\mu=0\) | \(\mathrm{(I)}\) | \(a=g\sqrt2,N=\dfrac{5mg}{\sqrt2}\) |
| \(\mathrm{(B)}\) | \(F_{\text{ext}}=mg,\mu=\dfrac12\) | \(\mathrm{(II)}\) | \(a=\dfrac{3g}{\sqrt2},N=\dfrac{5mg}{\sqrt2}\) |
| \(\mathrm{(C)}\) | \(F_{\text{ext}}=4mg,\mu=0\) | \(\mathrm{(III)}\) | \(a=\dfrac{g}{\sqrt2},N=\sqrt2mg\) |
| \(\mathrm{(D)}\) | \(F_{\text{ext}}=4mg,\mu=\dfrac15\) | \(\mathrm{(IV)}\) | \(a=0,N=\sqrt2mg\) |
| 1. | \(\mathrm{A\text-IV,B\text-III,C\text-I,D\text-II}\) |
| 2. | \(\mathrm{A\text-IV,B\text-IV,C\text-II,D\text-I}\) |
| 3. | \(\mathrm{A\text-III,B\text-IV,C\text-II,D\text-I}\) |
| 4. | \(\mathrm{A\text-III,B\text-III,C\text-I,D\text-II}\) |
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| 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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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. | \(N\) increases as \(F\) increases. |
| 2. | \(N\) does not act through the center of the block. |
| 3. | \(f\) is greater than \(F.\) |
| 4. | \(f\) acts through the centre of the block. |
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1. \(8\) N
2. \(6\) N
3. \(4\) N
4. \(2\) N
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1. \(10\) N
2. \(10 \sqrt 2\) N
3. \(5 \sqrt 2\) N
4. \(5\) N
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1. \(\mu_s=0.4\)
2. \(\mu_s=\mu{\small_k}=0.4\)
3. \(\mu{\small_ k}=0.4\)
4. \(\mu_s\geq0.4\)
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1. \(S_A=2S_B\)
2. \(S_B=2S_A\)
3. \(4S_A=S_B\)
4. \(S_A=S_B\)
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