Q. No.A \(0.5~\text{kg}\) mass is in contact against the inner wall of a cylindrical drum of radius \(4~\text{m}\) rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is \(5~ \text{rad/s}.\) \(\left(\text { Take } g=10 ~\text{m/s}^2\right).\)
1. \(0.1\)
2. \(0.5\)
3. \(0.7\)
4. \(0.3\)
1. \(0.1\)
2. \(0.5\)
3. \(0.7\)
4. \(0.3\)
Subtopic: Friction |
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A block takes \(t\) time to slide down a plane inclined at \(45^\circ\) to the horizontal. If the surface is made smooth (frictionless), the block takes time \(\dfrac{t}{2}\) to slide down the plane. The coefficient of friction between the block and the inclined plane is \(\left(\frac{\alpha}{100}\right).\) The value of \(\alpha\) is:
1. \(100\)
2. \(75\)
3. \(125\)
4. \(130\)
1. \(100\)
2. \(75\)
3. \(125\)
4. \(130\)
Subtopic: Friction |
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Two blocks (\(P\) and \(Q\)
1. \(0.33\)
2. \(0.67\)
3. \(1\)
4. \(0.5\)
1. \(0.33\)
2. \(0.67\)
3. \(1\)
4. \(0.5\)
Subtopic: Friction |
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A mass of \(1~\text{kg}\) is kept on a inclined plane with \(30^\circ\) inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of \(4~\text{m/s}\). The work done by the frictional force in time \(2~\text{s}\) is: (in J) (Take \(g=10~\text{m/s}^2\))
1. \(20\)
2. \(25\)
3. \(30\)
4. \(10\)
1. \(20\)
2. \(25\)
3. \(30\)
4. \(10\)
Subtopic: Friction |
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A solid cylinder having radius \(R\) and length \(L\) is slipping on a rough horizontal plane. At time \(t=0\) the cylinder has a translational velocity \(v_0=49~\text{m/s}\), perpendicular to axis and a rotational velocity \(\dfrac{v_0}{4R}\) about the centre. The time taken by the cylinder to start rolling is: (in seconds)
(coefficient of kinetic friction \(\mu_K=0.25 \text { and } g=9.8 ~\text{m/s}^2\))
1. \(15\)
2. \(5\)
3. \(10\)
4. \(7.5\)
(coefficient of kinetic friction \(\mu_K=0.25 \text { and } g=9.8 ~\text{m/s}^2\))
1. \(15\)
2. \(5\)
3. \(10\)
4. \(7.5\)
Subtopic: Friction |
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The time taken by a block of mass \(m\) \(50 \%\) \(45^{\circ}\)
1. \(3/4\)
2. \(2/3\)
3. \(5/9\)
4. \(4/9\)
1. \(3/4\)
2. \(2/3\)
3. \(5/9\)
4. \(4/9\)
Subtopic: Friction |
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A large drum having radius \(R\) is spinning around its axis with angular velocity \(\omega\), as shown in figure. The minimum value of \(\omega\) so that a body of mass \(M\) remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass \(M\) is \( \mu \), is:
1. \(\sqrt{\dfrac{\mu g}{R}}~\)
2. \(\sqrt{\dfrac{2 g}{\mu R}}~\)
3. \(\sqrt{\dfrac{g}{2 \mu R}}~\)
4. \(\sqrt{\dfrac{g}{\mu R}}~\)
1. \(\sqrt{\dfrac{\mu g}{R}}~\)
2. \(\sqrt{\dfrac{2 g}{\mu R}}~\)
3. \(\sqrt{\dfrac{g}{2 \mu R}}~\)
4. \(\sqrt{\dfrac{g}{\mu R}}~\)
Subtopic: Friction |
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In the given figure the blocks \(A,B~\text{and}~C\) weights \(4 ~\text{kg}\), \(6~ \text{kg}\) and \(8~\text{kg}\) respectively. The co-efficient of sliding friction between any two surfaces is \(0.5.\) The force \(\overrightarrow{{F}}\) required to slide the block \(C\) with constant speed is: (in N) (Used \(g=10 ~\text{m/s}^2\))
1. \(190\)
2. \(210\)
3. \(230\)
4. \(180\)
1. \(190\)
2. \(210\)
3. \(230\)
4. \(180\)
Subtopic: Friction |
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A block of mass \(5~\text{kg}\) is moving on inclined plane which makes an angle of \(30^\circ\) with the horizontal. Friction coefficient between the block and inclined plane surface is \(\dfrac{\sqrt{3}}{2} .\) The force to be applied on the block so that the block will move down without acceleration is: (in N)
1. \(25\)
2. \(12.5\)
3. \(7.5\)
4. \(15\)
1. \(25\)
2. \(12.5\)
3. \(7.5\)
4. \(15\)
Subtopic: Friction |
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A cubie block of mass \(m\) is sliding down on an inclined plane at \(60^\circ \) with an acceleration \(\dfrac{g}{2},\) the value of coefficient of kinetic friction is:
1. \(\sqrt {\dfrac{3}{2} }~\)
2. \(\sqrt 3-1~\)
3. \(1- \sqrt {\dfrac{3}{2} }~\)
4. \(\sqrt {\dfrac{2}{3}}~\)
1. \(\sqrt {\dfrac{3}{2} }~\)
2. \(\sqrt 3-1~\)
3. \(1- \sqrt {\dfrac{3}{2} }~\)
4. \(\sqrt {\dfrac{2}{3}}~\)
Subtopic: Friction |
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