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

2019 34 questions

1. Q522019 · 12 Jan 2019 · Shift 2

   A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be :

   1. A.2.0
   2. B.1.2
   3. C.0.1
   4. D.0.4
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   Answer: A

2. Q512019 · 11 Jan 2019 · Shift 2

   The magnitude of torque on a particle of mass $1\text{ kg}$ is $2.5\text{ Nm}$ about the origin. If the force acting on it is $1\text{ N}$, and the distance of the particle from the origin is $5\text{ m}$, the angle between the force and the position vector is (in radians) :

   1. A.$\frac{\pi }{8}$
   2. B.$\frac{\pi }{6}$
   3. C.$\frac{\pi }{4}$
   4. D.$\frac{\pi }{3}$
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   Answer: B

3. Q532019 · 11 Jan 2019 · Shift 2
   
   1. A.$3{\mathrm{MR}}^2$
   2. B.${\mathrm{MR}}^2$
   3. C.$\frac{2}{3}{\mathrm{MR}}^2$
   4. D.$\frac{4}{5}{\mathrm{MR}}^2$
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   Answer: A

4. Q572019 · 11 Jan 2019 · Shift 2
   
   1. A.$16{\text{ rad/s}}^2$
   2. B.$20{\text{ rad/s}}^2$
   3. C.$10{\text{ rad/s}}^2$
   4. D.$12{\text{ rad/s}}^2$
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   Answer: A

5. Q352019 · 9 Jan 2019 · Shift 1

   Three charges $+Q$, $q$, $+Q$ are placed respectively, at distance, 0, $d/2$ and $d$ from the origin, on the x-axis. If the net force experienced by $+Q$, placed at $x=0$, is zero, then value of $q$ is :

   1. A.$-\frac{Q}{4}$
   2. B.$+\frac{Q}{2}$
   3. C.$+\frac{Q}{4}$
   4. D.$-\frac{Q}{2}$
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   Answer: A

6. Q412019 · 9 Jan 2019 · Shift 1
   
   1. A.$45^{\circ }\mathrm{C}$
   2. B.$75^{\circ }\mathrm{C}$
   3. C.$60^{\circ }\mathrm{C}$
   4. D.$35^{\circ }\mathrm{C}$
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   Answer: A

7. Q472019 · 9 Jan 2019 · Shift 1
   
   1. A.$\frac{3k{\theta }_0^2}{l}$
   2. B.$\frac{2k{\theta }_0^2}{l}$
   3. C.$\frac{k{\theta }_0^2}{l}$
   4. D.$\frac{k{\theta }_0^2}{2l}$
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   Answer: C

8. Q482019 · 9 Jan 2019 · Shift 1

   If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is :

   1. A.$\frac{L}{m}$
   2. B.$\frac{4L}{m}$
   3. C.$\frac{L}{2m}$
   4. D.$\frac{2L}{m}$
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   Answer: C

9. Q532019 · 9 Jan 2019 · Shift 1

   A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion $\alpha {/}^{\circ }\mathrm{C}$. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by $\Delta T\text{ K}$. Young's modulus, Y, for this metal is :

   1. A.$\frac{F}{A\alpha \Delta T}$
   2. B.$\frac{F}{A\alpha (\Delta T-273)}$
   3. C.$\frac{F}{2A\alpha \Delta T}$
   4. D.$\frac{2F}{A\alpha \Delta T}$
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   Answer: A