A uniform rod of mass \(20~\text{kg}\) and length \(5\text{ m}\) leans against a smooth vertical wall making an angle of \(60^{\circ}\) with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is: (take \(g=10~\text{m/s}^2\) )
| 1. | \(200 ~\text{N}\) | 2. | \(200 \sqrt{3} ~\text{N}\) |
| 3. | \(100 ~\text{N}\) | 4. | \(100 \sqrt{3} ~\text{N}\) |
Subtopic: Torque |
Level 3: 35%-60%
NEET - 2025
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A sphere of radius \(R\) is cut from a larger solid sphere of radius \(2R\) as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the \(Y\)-axis is:
| 1. | \(\dfrac{7}{57}\) | 2. | \(\dfrac{7}{64}\) |
| 3. | \(\dfrac{7}{8}\) | 4. | \(\dfrac{7}{40}\) |
Subtopic: Moment of Inertia |
Level 3: 35%-60%
NEET - 2025
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The radius of Martian orbit around the sun is about \(4\) times the radius of the orbit of mercury. The Martian year is \(687\) earth days. Then which of the following is the length of \(1\) year on mercury?
1. \(172\) earth days
2. \(124\) earth days
3. \(88\) earth days
4. \(225\) earth days
1. \(172\) earth days
2. \(124\) earth days
3. \(88\) earth days
4. \(225\) earth days
Subtopic: Kepler's Laws |
56%
Level 3: 35%-60%
NEET - 2025
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A body weight \(48~\text{N}\) on the surface of the earth. The gravitational force experienced by the body due to the Earth at a height equal to one-third the radius of the Earth from its surface is:
| 1. | \(32~\text N\) | 2. | \(36~\text N\) |
| 3. | \(16~\text N\) | 4. | \(27~\text N\) |
Subtopic: Acceleration due to Gravity |
Level 3: 35%-60%
NEET - 2025
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Consider a water tank shown in the figure. It has one wall at \(x=L\) and can be taken to be very wide in the \(z\) direction. When filled with a liquid of surface tension \(S\) and density \(\rho,\) the liquid, surface makes angle \(\theta_{0}\left(\theta_0 \ll 1\right)\) with the \(x\text-\)axis at \(x=L.\) If \(y(x)\) is the height of the surface then the equation for \(y(x)\) is:
(take \(\theta(x)=\sin \theta(x)=\tan \theta(x)=\dfrac{d y}{d x}, g\) is the acceleration due to gravity)
(take \(\theta(x)=\sin \theta(x)=\tan \theta(x)=\dfrac{d y}{d x}, g\) is the acceleration due to gravity)
| 1. | \(\dfrac{d^2 y}{d x^2}=\sqrt{\dfrac{\rho g}{S}}\) | 2. | \(\dfrac{d y}{d x}=\sqrt{\dfrac{\rho g}{S}} x\) |
| 3. | \(\dfrac{d^2 y}{d x^2}=\dfrac{\rho g}{S} x\) | 4. | \(\dfrac{d^2 y}{d x^2}=\dfrac{\rho g}{S} y\) |
Subtopic: Surface Tension |
Level 4: Below 35%
NEET - 2025
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Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity \(2K\) while that in the middle has thermal conductivity \(K\). The left end of the combination is maintained at temperature \(3T\) and the right end at \(T.\) The rods are thermally insulated from outside. In the steady state, temperature at the left junction is \(T_1\) and that at the right junction is \(T_2\). The ratio \(\dfrac{T_1}{T_2}\) is:
| 1. | \(\dfrac{5}{3}\) | 2. | \(\dfrac{5}{4}\) |
| 3. | \(\dfrac{3}{2}\) | 4. | \(\dfrac{4}{3}\) |
Subtopic: Conduction |
Level 3: 35%-60%
NEET - 2025
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Two gases \(A\) and \(B\) are filled at the same pressure in separate cylinders with movable pistons of radius \(r_A\) and \(r_B,\) respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas \(A\) and \(B\) are displaced by \(16~ \text{cm}\) and \(9~ \text{cm},\) respectively. If the change in their internal energy is the same, then the ratio \(r_A / r_B\) is equal to:
| 1. | \(\dfrac{2}{\sqrt{3}}\) | 2. | \(\dfrac{\sqrt{3}}{2}\) |
| 3. | \(\dfrac{4}{3}\) | 4. | \(\dfrac{3}{4}\) |
Subtopic: Work Done by a Gas |
Level 3: 35%-60%
NEET - 2025
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A container has two chambers of volumes \(V_1=2~\text{litres} \) and \(V_2=3~\text{litres} \) separated by a partition made of a thermal insulator. The chambers contains \( n_1=5 \) and \( n_2=4 \) moles of ideal gas at pressures \(p_1=1~\text{atm} \) and \(p_2=2~\text{atm}, \) respectively. When the partition is removed, the mixture attains an equilibrium pressure of:
| 1. | \(1.4 ~\text{atm} \) | 2. | \(1.8 ~\text{atm} \) |
| 3. | \(1.3 ~\text{atm} \) | 4. | \(1.6 ~\text{atm} \) |
Subtopic: Ideal Gas Equation |
Level 3: 35%-60%
NEET - 2025
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An oxygen cylinder of volume \(30\) litre has \(18.20\) moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to \(11\) atmospheric pressure at temperature \(27^{\circ} \text{C}.\) The mass of the oxygen withdrawn from the cylinder is nearly equal to:
\([\)Given, \(R=\frac{100}{12}~ \text{J} \mathrm{~mol}^{-1} {~\text K}^{-1},\) and molecular mass of \(O_2=32,\) \(1\) atm pressure \(\left.=1.01 \times 10^5 \mathrm{~N} / \mathrm{m}\right]\)
1. \(0.116\text{ kg}\)
2. \(0.156\text{ kg}\)
3. \(0.125\text{ kg}\)
4. \(0.144\text{ kg}\)
\([\)Given, \(R=\frac{100}{12}~ \text{J} \mathrm{~mol}^{-1} {~\text K}^{-1},\) and molecular mass of \(O_2=32,\) \(1\) atm pressure \(\left.=1.01 \times 10^5 \mathrm{~N} / \mathrm{m}\right]\)
1. \(0.116\text{ kg}\)
2. \(0.156\text{ kg}\)
3. \(0.125\text{ kg}\)
4. \(0.144\text{ kg}\)
Subtopic: Ideal Gas Equation |
Level 4: Below 35%
NEET - 2025
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In an oscillating spring mass system, a spring is connected to a box filled with the sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency \(\omega~(t)\) and average amplitude \(A~(t)\) of the system changes with time \(t.\) Which of the following options systemically depicts these changes correctly?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Spring mass system |
Level 3: 35%-60%
NEET - 2025
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