List of top Physics Questions on System of Particles & Rotational Motion

A cylindrical tube $AB$ of length $l$, closed at both ends, contains an ideal gas of $1$ mol having molecular weight $M$. The tube is rotated in a horizontal plane with constant angular velocity $\omega$ about an axis perpendicular to $AB$ and passing through the edge at end $A$, as shown in the figure. If $P_A$ and $P_B$ are the pressures at $A$ and $B$ respectively, then (consider the temperature to be same at all points in the tube)

As shown in the figure, radius of gyration about the axis shown in $\sqrt{n}$ cm for a solid sphere. Find 'n'.

When rod becomes horizontal find its angular velocity. It is pivoted at point A as shown.

The temperature of a body in air falls from $ 40^\circ \text{C} $ to $ 24^\circ \text{C} $ in 4 minutes. The temperature of the air is $ 16^\circ \text{C} $. The temperature of the body in the next 4 minutes will be:

The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in a similar way. The moment of inertia of a solid sphere which has the same radius as the disc and rotating in similar way, is $ n $ times higher than the moment of inertia of the given ring. Here, $ n = $:

The increase in pressure required to decrease the volume of a water sample by 0.2percentage is $ P \times 10^5 \, \text{Nm}^{-2} $. Bulk modulus of water is $ 2.15 \times 10^9 \, \text{Nm}^{-2} $. The value of $ P $ is ________________.

A string of length $ L $ is fixed at one end and carries a mass of $ M $ at the other end. The mass makes $ \frac{3}{\pi} $ rotations per second about the vertical axis passing through the end of the string as shown. The tension in the string is ________________ ML.

Two iron solid discs of negligible thickness have radii $ R_1 $ and $ R_2 $ and moment of inertia $ I_1 $ and $ I_2 $, respectively. For $ R_2 = 2R_1 $, the ratio of $ I_1 $ and $ I_2 $ would be $ \frac{1}{x} $, where $ x $ is:

The center of mass of a thin rectangular plate (fig - x) with sides of length $ a $ and $ b $, whose mass per unit area ($ \sigma $) varies as $ \sigma = \sigma_0 \frac{x}{ab} $ (where $ \sigma_0 $ is a constant), would be

The increase in pressure required to decrease the volume of a water sample by 0.2percentage is $ P \times 10^5 \, \text{Nm}^{-2} $. Bulk modulus of water is $ 2.15 \times 10^9 \, \text{Nm}^{-2} $. The value of $ P $ is ………..

A string of length $ L $ is fixed at one end and carries a mass of $ M $ at the other end. The mass makes $ \frac{3}{\pi} $ rotations per second about the vertical axis passing through the end of the string as shown. The tension in the string is \_\_\_\_ ML.

The temperature of a body in air falls from $ 40^\circ \text{C} $ to $ 24^\circ \text{C} $ in 4 minutes. The temperature of the air is $ 16^\circ \text{C} $. The temperature of the body in the next 4 minutes will be:

The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at rest on the river bank is _________ cm. (Take $ g = 10 \, {m/s}^2 $).

A container of fixed volume contains a gas at 27°C. To double the pressure of the gas, the temperature of the gas should be raised to …. C.

Match List - I with List - II: List - I:

(A) Electric field inside (distance $ r > 0 $ from center) of a uniformly charged spherical shell with surface charge density $ \sigma $, and radius $ R $.
(B) Electric field at distance $ r > 0 $ from a uniformly charged infinite plane sheet with surface charge density $ \sigma $.
(C) Electric field outside (distance $ r > 0 $ from center) of a uniformly charged spherical shell with surface charge density $ \sigma $, and radius $ R $.
(D) Electric field between two oppositely charged infinite plane parallel sheets with uniform surface charge density $ \sigma $.

List - II:

(I) $ \frac{\sigma}{\epsilon_0} $
(II) $ \frac{\sigma}{2\epsilon_0} $
(III) 0
(IV) $ \frac{\sigma}{\epsilon_0 r^2} $

Choose the correct answer from the options given below:

Two iron solid discs of negligible thickness have radii $ R_1 $ and $ R_2 $ and moment of inertia $ I_1 $ and $ I_2 $, respectively. For $ R_2 = 2R_1 $, the ratio of $ I_1 $ and $ I_2 $ would be $ \frac{1}{x} $, where $ x $ is:

The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in a similar way. The moment of inertia of a solid sphere which has the same radius as the disc and rotating in similar way, is $ n $ times higher than the moment of inertia of the given ring. Here, $ n = $:

The center of mass of a thin rectangular plate (fig - x) with sides of length $ a $ and $ b $, whose mass per unit area ($ \sigma $) varies as $ \sigma = \sigma_0 \frac{x}{ab} $ (where $ \sigma_0 $ is a constant), would be

During an elastic collision between two bodies, which of the following statements are correct?

A body of mass 10 kg is moving with a speed of 5 m/s. What is the momentum of the body?

A solid cylinder of mass 2 kg, length 40 cm and radius 10 cm is placed in contact with a solid sphere of mass 0.5 kg and radius 10 cm such that the centres of the two bodies lie along the geometrical axis of the cylinder. The distance of the centre of mass of the system of two bodies from the centre of the sphere is

A thin uniform circular disc of mass $\frac{10}{\pi^2}$ kg and radius 2 m is rotating about an axis passing through its centre and perpendicular to its plane. The work done to increase the angular speed of the disc from 90 rev/min to 120 rev/min is

A body of mass 'm' moving with a velocity of 'v' collides head on with another body of mass '2m' at rest. If the coefficient of restitution between the two bodies is 'e', then the ratio of the velocities of the two bodies after collision is

A particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^2 = 1 + t^2$.
Its acceleration at any time $t$ is $x^{-n}$ where $n =$ ____.

A particle is moving in circular path of radius r speed v such that speed is proportional to radius as $V∝ r^{\frac{3}{2}}$. Then how does time period of revolution depends on r i.e Trn then $n$ is.