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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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Level 1: 80%+
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Two blocks of masses \(2~\text{kg}\) and \(1~\text{kg}\) respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass in \(2~\text{s}\) is: (in m) (Take \(g=10 ~\text{m/s}^2\)
1. \(3.33\)
2. \(3.12\)
3. \(2.22\)
4. \(1.42\)
1. \(3.33\)
2. \(3.12\)
3. \(2.22\)
4. \(1.42\)
Subtopic: Tension & Normal Reaction |
Level 3: 35%-60%
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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 |
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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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Level 2: 60%+
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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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Level 2: 60%+
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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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Level 1: 80%+
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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 |
54%
Level 3: 35%-60%
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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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Level 2: 60%+
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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 2: 60%+
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Two wires as shown in the figure below, made of steel and have breaking stress of \(12 \times 10^8 ~\text{N/m}^2\) Area of cross-section of upper wire is \(0.008~\text{cm}^2\) and of lower wire is \(0.004~\text{cm}^2\). The maximum mass that can be added to pan without breaking any wire is: (in kg)
\(\left(\text { take } g=10 ~\text{m/s}^2\right)~\)
1. \(56\)
2. \(38\)
3. \(96\)
4. \(5.6\)
\(\left(\text { take } g=10 ~\text{m/s}^2\right)~\)
1. \(56\)
2. \(38\)
3. \(96\)
4. \(5.6\)
Subtopic: Tension & Normal Reaction |
78%
Level 2: 60%+
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