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

2012 5 questions

1. Q372012 · 26 May 2012 · Shift 1

   A thick-walled hollow sphere has outside radius $R_0$. It rolls down an incline without slipping and its speed at the bottom is $v_0$. Now the incline is waxed, so that it is practically frictionless and the sphere is observed to slide down (without any rolling). Its speed at the bottom is observed to be $5v_0/4$. The radius of gyration of the hollow sphere about an axis through its centre is

   1. A.$3R_0/2$
   2. B.$3R_0/4$
   3. C.$9R_0/16$
   4. D.$3R_0$
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   Answer: B

2. Q372012 · 12 May 2012 · Shift 1
   
   1. A.$\sqrt{2gh}$
   2. B.$\sqrt{\frac{7}{5}gh}$
   3. C.$\sqrt{\frac{7}{2}gh}$
   4. D.$\sqrt{\frac{10}{7}gh}$
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   Answer: D

3. Q382012 · 12 May 2012 · Shift 1

   This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: When moment of inertia $I$ of a body rotating about an axis with angular speed $\omega$ increases, its angular momentum $L$ is unchanged but the kinetic energy $K$ increases if there is no torque applied on it. Statement 2: $L=I\omega$, kinetic energy of rotation $=\frac{1}{2}I{\omega }^2$

   1. A.Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.
   2. B.Statement 1 is false, Statement 2 is true.
   3. C.Statement 1 is true, Statement 2 is true, Statement 2 is correct explanation of the Statement 1.
   4. D.Statement 1 is true, Statement 2 is false.
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   Answer: B

4. Q322012 · 7 May 2012 · Shift 1
   
   1. A.$v_A=v_B=0.5m/s$
   2. B.$v_A=0.5m/s<v_B$
   3. C.$v_A=0.5m/s>v_B$
   4. D.$v_A=v_B=2m/s$
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   Answer: A

5. Q362012 · 7 May 2012 · Shift 1

   A circular hole of diameter $R$ is cut from a disc of mass $M$ and radius $R$; the circumference of the cut passes through the centre of the disc. The moment of inertia of the remaining portion of the disc about an axis perpendicular to the disc and passing through its centre is

   1. A.$\left(\frac{15}{32}\right)M{R}^2$
   2. B.$\left(\frac{1}{8}\right)M{R}^2$
   3. C.$\left(\frac{3}{8}\right)M{R}^2$
   4. D.$\left(\frac{13}{32}\right)M{R}^2$
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   Answer: D