Centre of Mass & Rotational Motion · JEE Main previous year questions

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2021 21 questions

Q512021 · 1 Sept 2021 · Shift 2· Numerical answer
The temperature of $3.00 mol$ of an ideal diatomic gas is increased by $40. 0^{\circ} C$ without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is $\frac{x}{10}$ . Then the value of x (round off to the nearest integer) is ____. (Given $R = 8.31 J mo l^{- 1} K^{- 1}$ )
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Answer: 25
Q572021 · 1 Sept 2021 · Shift 2· Numerical answer
A steel rod with $y = 2.0 \times 1 0^{11} N m^{- 2}$ and $α = 1 0^{- 5}^{\circ} C^{- 1}$ of length $4 m$ and area of cross-section $10 c m^{2}$ is heated from $0^{\circ} C$ to $40 0^{\circ} C$ without being allowed to extend. The tension produced in the rod is $x \times 1 0^{5} N$ where the value of x is ____.
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Answer: 8
Q582021 · 1 Sept 2021 · Shift 2· Numerical answer
A $2 kg$ steel rod of length $0.6 m$ is clamped on a table vertically at its lower end and is free to rotate in vertical plane. The upper end is pushed so that the rod falls under gravity, ignoring the friction due to clamping at its lower end, the speed of the free end of rod when it passes through its lowest position is ____ $m s^{- 1}$ . (Take $g = 10 m s^{- 2}$ )
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Answer: 6
Q392021 · 26 Aug 2021 · Shift 2
1. A. $14.9 kg/m^{3}$
2. B. $7.5 \times 1 0^{1} kg/m^{3}$
3. C. $7.5 \times 1 0^{2} kg/m^{3}$
4. D. $1.49 \times 1 0^{2} kg/m^{3}$
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Answer: D
Q522021 · 26 Aug 2021 · Shift 2· Numerical answer
A source of light is placed in front of a screen. Intensity of light on the screen is I. Two Polaroids $P_{1}$ and $P_{2}$ are so placed in between the source of light and screen that the intensity of light on screen is $I /2$ . $P_{2}$ should be rotated by an angle of (degrees) so that the intensity of light on the screen becomes $\frac{3 I}{8}$ .
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Answer: 30
Q572021 · 26 Aug 2021 · Shift 2· Numerical answer
A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field 20 mT. The torque acting on the coil when a current of 0.2 A is passed through it and its plane becomes parallel to the magnetic field will be $x \times 1 0^{- 5} Nm$ . The value of x is ...............
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Answer: 3
Q322021 · 25 Jul 2021 · Shift 1
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Moment of inertia of a circular disc of mass 'M' and radius 'R' about X, Y axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be $I_{x}$ , $I_{y}$ and $I_{z}$ respectively. The respectively radii of gyration about all the three axes will be the same. Reason R : A rigid body making rotational motion has fixed mass and shape. In the light of the above statements, choose the most appropriate answer from the options given below :
1. A.Both A and R are correct but R is NOT the correct explanation of A.
2. B.A is not correct but R is correct.
3. C.A is correct but R is not correct.
4. D.Both A and R are correct and R is the correct explanation of A.
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Answer: B
Q572021 · 25 Jul 2021 · Shift 2· Numerical answer
A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in 10 s is ____ $π \times 1 0^{- 1}$ Nm.
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Answer: 4
Q352021 · 22 Jul 2021 · Shift 2
Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation is
1. A.All of them will have same velocity.
2. B.The ring has greatest and the cylinder has the least velocity of the centre of mass at the bottom of the inclined plane.
3. C.The sphere has the greatest and the ring has the least velocity of the centre of mass at the bottom of the inclined plane.
4. D.The cylinder has the greatest and the sphere has the least velocity of the centre of mass at the bottom of the inclined plane.
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Answer: C
Q562021 · 22 Jul 2021 · Shift 2· Numerical answer
The position of the centre of mass of a uniform semi-circular wire of radius 'R' placed in x-y plane with its centre at the origin and the line joining its ends as x-axis is given by $(0, \frac{x R}{π})$ . Then, the value of $∣ x ∣$ is ________.
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Answer: 2
Q592021 · 22 Jul 2021 · Shift 2· Numerical answer
The centre of a wheel rolling on a plane surface moves with a speed $v_{0}$ . A particle on the rim of the wheel at the same level as the centre will be moving at a speed $x v_{0}$ . Then the value of x is ________.
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Answer: 2
Q412021 · 20 Jul 2021 · Shift 1
1. A. $686$
2. B. $684$
3. C. $714$
4. D. $716$
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Answer: A
Q342021 · 18 Mar 2021 · Shift 1
A thin circular ring of mass M and radius r is rotating about its axis with an angular speed $ω$ . Two particles having mass m each are now attached at diametrically opposite points. The angular speed of the ring will become :
1. A. $ω \frac{M}{M + m}$
2. B. $ω \frac{M + 2 m}{M}$
3. C. $ω \frac{M}{M + 2 m}$
4. D. $ω \frac{M - 2 m}{M + 2 m}$
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Answer: C
Q322021 · 18 Mar 2021 · Shift 2
If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately : [Take $g = 10 m s^{- 2}$ , the radius of earth, $R = 6400 \times 1 0^{3} m$ , Take $π = 3.14$ ]
1. A.84 minutes
2. B.1200 minutes
3. C.60 minutes
4. D.does not change
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Answer: A
Q362021 · 18 Mar 2021 · Shift 2
The angular momentum of a planet of mass $M$ moving around the sun in an elliptical orbit is $L$ . The magnitude of the areal velocity of the planet is :
1. A. $\frac{2 L}{M}$
2. B. $\frac{L}{2 M}$
3. C. $\frac{L}{M}$
4. D. $\frac{4 L}{M}$
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Answer: B
Q382021 · 18 Mar 2021 · Shift 2
Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the center is :
1. A. $\frac{1}{4} \frac{M L ^{2}}{π ^{2}}$
2. B. $\frac{1}{2} \frac{M L ^{2}}{π ^{2}}$
3. C. $\frac{2}{5} \frac{M L ^{2}}{π ^{2}}$
4. D. $\frac{M L ^{2}}{π ^{2}}$
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Answer: D
Q462021 · 18 Mar 2021 · Shift 2
An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is $S_{1}$ and that of the other part is $S_{2}$ . Given that $S_{1} > S_{2}$ . If the piston is removed then the total entropy of the system will be :
1. A. $S_{1} - S_{2}$
2. B. $\frac{S _{1}}{S _{2}}$
3. C. $S_{1} \times S_{2}$
4. D. $S_{1} + S_{2}$
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Answer: D
Q582021 · 18 Mar 2021 · Shift 2· Numerical answer
An infinite number of point charges, each carrying $1 μ C$ charge, are placed along the y-axis at $y = 1 m, 2 m, 4 m, 8 m ..............$ The total force on a 1C point charge, placed at the origin, is $x \times 1 0^{3} N$ . The value of x, to the nearest integer, is ____. [Take $\frac{1}{4 π ε _{0}} = 9 \times 1 0^{9} N m^{2} / C^{2}$ ]
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Answer: 12
Q372021 · 16 Mar 2021 · Shift 1
1. A. $3 m l^{2}$
2. B. $2 m l^{2}$
3. C. $m l^{2}$
4. D. $3 m l^{2}$
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Answer: D
Q332021 · 26 Feb 2021 · Shift 1
Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :
1. A. $\frac{4}{5} m a^{2}$
2. B. $\frac{8}{5} m a^{2} + m b^{2}$
3. C. $\frac{4}{5} m a^{2} + 2 m b^{2}$
4. D. $\frac{8}{5} m a^{2} + 2 m b^{2}$
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Answer: D
Q462021 · 26 Feb 2021 · Shift 2
A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance 'h', the square of angular velocity of wheel will be :
1. A. $\frac{2 m g h}{I + 2 m r ^{2}}$
2. B. $\frac{2 m g h}{I + m r ^{2}}$
3. C. $2 g h$
4. D. $\frac{2 g h}{I + m r ^{2}}$
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Answer: B