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

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2023 41 questions

Q312023 · 31 Jan 2023 · Shift 2
For a solid rod, the Young's modulus of elasticity is $3.2 \times 1 0^{11} Nm^{- 2}$ and density is $8 \times 1 0^{3} kg m^{- 3}$ . The velocity of longitudinal wave in the rod will be.
1. A. $3.65 \times 1 0^{3} ms^{- 1}$
2. B. $6.32 \times 1 0^{3} ms^{- 1}$
3. C. $18.96 \times 1 0^{3} ms^{- 1}$
4. D. $145.75 \times 1 0^{3} ms^{- 1}$
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Answer: B
Q322023 · 31 Jan 2023 · Shift 2
Heat energy of $735 J$ is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be :
1. A. $572 J$
2. B. $441 J$
3. C. $525 J$
4. D. $735 J$
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Answer: C
Q442023 · 31 Jan 2023 · Shift 2
Match List I with List II | LIST I | LIST II | | :--- | :--- | | A. Angular momentum | I. $[ML^{2} T^{- 2}]$ | | B. Torque | II. $[ML^{- 2} T^{- 2}]$ | | C. Stress | III. $[ML^{2} T^{- 1}]$ | | D. Pressure gradient | IV. $[ML^{- 1} T^{- 2}]$ | Choose the correct answer from the options given below:
1. A.A - I, B - IV, C - III, D - II
2. B.A - III, B - I, C - IV, D - II
3. C.A - IV, B - II, C - I, D - III
4. D.A - II, B - III, C - IV, D - I
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Answer: B
Q572023 · 31 Jan 2023 · Shift 2· Numerical answer
Two discs of same mass and different radii are made of different materials such that their thicknesses are $1 cm$ and $0.5 cm$ respectively. The densities of materials are in the ratio $3 : 5$ . The moment of inertia of these discs respectively about their diameters will be in the ratio of $\frac{x}{6}$ . The value of $x$ is ___________.
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Answer: 5
Q552023 · 30 Jan 2023 · Shift 1· Numerical answer
A thin uniform rod of length $2 m$ , cross sectional area ' $A$ ' and density ' $d$ ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $ω$ . If value of $ω$ in terms of its rotational kinetic energy $E$ is $\frac{α E}{A d}$ then value of $α$ is ___________.
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Answer: 3
Q522023 · 29 Jan 2023 · Shift 1· Numerical answer
A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be ____ $m s^{- 1}$ .
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Answer: 40
Q552023 · 29 Jan 2023 · Shift 1· Numerical answer
As shown in the figure, three identical polaroids $P_{1}$ , $P_{2}$ and $P_{3}$ are placed one after another. The pass axis of $P_{2}$ and $P_{3}$ are inclined at angle of $6 0^{\circ}$ and $9 0^{\circ}$ with respect to axis of $P_{1}$ . The source S has an intensity of 256 $\frac{W}{m ^{2}}$ . The intensity of light at point O is ____ $\frac{W}{m ^{2}}$ .
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Answer: 24
Q512023 · 29 Jan 2023 · Shift 2· Numerical answer
A particle of mass 100 g is projected at time t = 0 with a speed 20 $m s^{- 1}$ at an angle $4 5^{\circ}$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time t = 2s is found to be $K kg m^{2} /s$ . The value of K is ____. (Take $g = 10 m s^{- 2}$ )
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Answer: 800
Q442023 · 25 Jan 2023 · Shift 1
1. A.90 N
2. B.240 N
3. C.30 N
4. D.300 N
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Answer: D
Q522023 · 25 Jan 2023 · Shift 1· Numerical answer
$I_{CM}$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. $I_{AB}$ is its moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance $\frac{2}{3}$ R from center. Where R is the radius of the disc. The ratio of $I_{AB}$ and $I_{CM}$ is $x : 9$ . The value of $x$ is ____.
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Answer: 17
Q572023 · 25 Jan 2023 · Shift 1· Numerical answer
As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of $4 5^{\circ}$ with the load axis. The length of wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to be $x \times 1 0^{4} N m^{- 2}$ . The value of $x$ is ____.
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Answer: 5
Q562023 · 25 Jan 2023 · Shift 2· Numerical answer
If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be $\frac{x}{7}$ . The value of $x$ is ____.
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Answer: 5
Q552023 · 24 Jan 2023 · Shift 1· Numerical answer
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Answer: 110
Q412023 · 24 Jan 2023 · Shift 2
1. A. $\frac{1}{2} B^{2} L^{2} ω$
2. B. $\frac{1}{2} BL^{2} ω$
3. C. $\frac{1}{4} BL^{2} ω$
4. D. $\frac{1}{4} B^{2} L ω$
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Answer: B
Q522023 · 24 Jan 2023 · Shift 2· Numerical answer
A body of mass 1kg begins to move under the action of a time dependent force $F = (t \hat{i} + 3 t^{2} \hat{j}) N$ , where $\hat{i}$ and $\hat{j}$ are the unit vectors along $x$ and $y$ axis. The power developed by above force, at the time t = 2s, will be _________ W.
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Answer: 100
Q542023 · 24 Jan 2023 · Shift 2· Numerical answer
A uniform solid cylinder with radius R and length L has moment of inertia $I_{1}$ , about the axis of the cylinder. A concentric solid cylinder of radius $R^{'} = \frac{R}{2}$ and length $L^{'} = \frac{L}{2}$ is carved out of the original cylinder. If $I_{2}$ is the moment of inertia of the carved out portion of the cylinder then $\frac{I _{1}}{I _{2}} =$ . (Both $I_{1}$ and $I_{2}$ are about the axis of the cylinder)
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Answer: 32