- 1(current)
Q. No.In the figure, the coefficient of friction between the floor and body \(B\) is \(0.1.\) The coefficient of friction between bodies \(B\) and \(A\) is \(0.2.\) A force \(F\) is applied as shown on \(B.\) The mass of \(A\) is \(m/2\) and of \(B\) is \(m.\)
| (a) | The bodies will move together if \(F = 0.25\text{mg}\) |
| (b) | The \(A\) will slip with \(B\) if \(F = 0.5\text{mg}\) |
| (c) | The bodies will move together if \(F = 0.5\text{mg}\) |
| (d) | The bodies will be at rest if \(F = 0.1\text{mg}\) |
| (e) | The maximum value of \(F\) for which the two bodies will move together is \(0.45\text{mg}\) |
Which of the following statement(s) is/are true?
1. (a), (b), (d), (e)
2. (a), (c), (d), (e)
3. (b), (c), (d)
4. (a), (b), (c)
Mass \(m_{1}\) moves on a slope making an angle \(\theta\) with the horizontal and is attached to mass \(m_{2}\) by a string passing over a frictionless pulley as shown in the figure. The coefficient of friction between \(m_{1}\) and the sloping surface is \(\mu\).
| (a) | If \(m_{2} > m_{1} \text{sin} \theta \), the body will move up the plane. |
| (b) | If \(m_{2} > m_{1} (\text{sin} \theta +\mu \text{cos} \theta)\), the body will move up the plane. |
| (c) | If \(m_{2} < m_{1} (\text{sin} \theta +\mu \text{cos} \theta)\), the body will move up the plane. |
| (d) | If \(m_{2} < m_{1} (\text{sin} \theta -\mu \text{cos} \theta)\), the body will move down the plane. |
| 1. | (a), (d) | 2. | (a), (c) |
| 3. | (c), (d) | 4. | (b), (d) |
In figure a body \(A\) of mass \(m\) slides on a plane inclined at angle \(\left(\theta_{1}\right)\) to the horizontal and \(\mu\) is the coefficient of friction between \(A\) and the plane. \(A\) is connected by a light string passing over a frictionless pulley to another body \(B,\) also of mass \(m\), sliding on a frictionless plane inclined at an angle \(\left(\theta_{2}\right)\) to the horizontal.
| (a) | A will never move up the plane |
| (b) | A will just start moving up the plane when \(\mu = \dfrac{{\sin} \left(\theta\right)_{2} - {\sin} \left(\theta\right)_{1}}{{\cos} \left(\theta\right)_{1}}\) |
| (c) | For \(A\) to move up the plane, \(\left(\theta\right)_{2}\) must always be greater than \(\left(\theta\right)_{1}\) |
| (d) | \(B\) will always slide down with a constant speed |
Which of the following statement/s is/are true?
| 1. | (b, c) | 2. | (c, d) |
| 3. | (a, c) | 4. | (a, d) |
a. A will never move up the plane.
b. A will just start moving up the plane when \(\mu=\frac{\sin \theta_2-\sin \theta_1}{\cos \theta_1} .\)
c. For A to move up the plane, \(\theta_2\) must always be greater than \(\theta_1\) .
d. B will always slide down with constant speed.
Choose the correct option:
1. (a), (d)
2. (a), (b), (d), (e)
3. (a), (b), (c)
4. (b), (c)
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Q. No.
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