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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 spherical ball of mass \(2~\text{kg}\) falls from a height of \(10~\text{m}\) and is brought to rest after penetrating \(10~\text {cm}\) into sand. The average force exerted by sand the ball is: (in N)
1. \(1980\)
2. \(2020\)
3. \(2000\)
4. \(1000\)
1. \(1980\)
2. \(2020\)
3. \(2000\)
4. \(1000\)
Subtopic: Types of Forces |
Level 3: 35%-60%
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The velocity at which \(6~\text{kg}\) mass (shown in figure) strikes the ground when it is released from a height of \(6~\text{m}\) above the ground is: (in m/s)
(Assume pulley is massless and string is light and inextensible. (Take \(g = 10~\text{m/s}^{2}\)))
1. \(7.74\)
2. \(7.20\)
3. \(6.55\)
4. \(4.50\)
(Assume pulley is massless and string is light and inextensible. (Take \(g = 10~\text{m/s}^{2}\)))
1. \(7.74\)
2. \(7.20\)
3. \(6.55\)
4. \(4.50\)
Subtopic: Application of Laws |
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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 lift of mass \(1600~\text{kg}\) is supported by thick iron wire. If the maximum stress which the wire can withstand is \(4 \times 10^{8}~\text{N/m}^2\) and its radius is \(4~\text{mm}\), then maximum acceleration the lift can take is: (in \(\text{m/s}^2\))
(take \(g = 10~\text{m/s}^{2} \) and \(\pi =3.14\))
1. \(2.56\)
2. \(3.89\)
3. \(4.32\)
4. \(5.16\)
(take \(g = 10~\text{m/s}^{2} \) and \(\pi =3.14\))
1. \(2.56\)
2. \(3.89\)
3. \(4.32\)
4. \(5.16\)
Subtopic: Tension & Normal Reaction |
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Three masses \( m_1 = 4~\text{kg}, m_2 = 4~\text{kg}\) and \(m_3 = 6~\text{kg}\) are suspended from a fixed smooth frictionless pully as shown in the figure below. The value of \(\dfrac{T_1}{T_2} \) is:
(take \(g= 10 ~\text {m/s}^2\))
1. \(\dfrac{5}{3} \)
2. \(\dfrac{2}{3} \)
3. \(\dfrac{3}{5}\)
4. \(\dfrac{2}{5}\)
(take \(g= 10 ~\text {m/s}^2\))
1. \(\dfrac{5}{3} \)
2. \(\dfrac{2}{3} \)
3. \(\dfrac{3}{5}\)
4. \(\dfrac{2}{5}\)
Subtopic: Tension & Normal Reaction |
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A wedge \(Y\) with mass of \(10 ~\text {kg}\) and all frictionless surfaces and the inclined surface making \(37^{\circ}\) with horizontal. A block \(X\) with mass \(2 ~\text {kg}\) is placed at the highest point of the wedge as shown in figure is at rest. At \(t=0\) wedge (\(Y\)) is pulled toward right with constant force (\( f\)) of \(24~\text{N}\). Taking the block \(X\) at rest at \(t=0\) the time taken by it to slide down \(8.8~\text{m}\) on the slope, while \( Y\) is on the move, is: (in \(\text{s}\))
(take \(\tan(37^{\circ})=\dfrac{3}{4}\) and \(g= 10~\text {m/s}^2\))
1. \(2\)
2. \(4\)
3. \(\sqrt{2}\)
4. \(2 \sqrt{2}\)
(take \(\tan(37^{\circ})=\dfrac{3}{4}\) and \(g= 10~\text {m/s}^2\))
1. \(2\)
2. \(4\)
3. \(\sqrt{2}\)
4. \(2 \sqrt{2}\)
Subtopic: Application of Laws |
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Level 3: 35%-60%
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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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Level 2: 60%+
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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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