Velocity of COM

Q.

Three point particles of mass $1kg,1.5kgand2.5kg$ are placed at three corners of a right triangle of sides $4.0cm,3.0cmand5.0cm$ as shown in the figure. The centre of mass of the system is at the point:

1. $0.9cm$ right and $2.0cm$ above $1kg$mass

2. $2.0cm$ right and $0.9cm$ above $1kg$ mass

3. $1.5cm$ right and $1.2cm$ above $1kg$ mass

4. $0.6cm$right and $2.0cm$ above $1kg$mass

Q. In the HCl molecule, the separation between the nuclei of hydrogen and chlorine atoms is 1.27 $\stackrel{\circ }{A}$. If the mass of a chlorine atom is 35.5 times that of a hydrogen atom, the centre of mass of the HCl molecule is at a distance of

1. $\frac{35.5\times 1.27}{36.5}\stackrel{\circ }{A}$ From the hydrogen atom
   
2. $\frac{35.5\times 1.27}{36.5}\stackrel{\circ }{A}$ From the chlorine atom
   
3. $\frac{1.27}{36.5}\stackrel{\circ }{A}$ From the hydrogen atom
4. $\frac{1.27}{36.5}\stackrel{\circ }{A}$ From the chlorine atom

Q. Assertion :For a system of particles under central force field, the total angular momentum is conserved. Reason: The torque acting on such a system is zero.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q. At first the rod is in unstable equilibrium in a horizontal uniform electric field strength E. Then we gently displace it from this position. Determine the maximum velocity attained by the ball that is closer to the axis in the subsequent motion:

1. $\sqrt{\frac{2QEL}{m}}$
2. $\sqrt{\frac{2QEL}{5m}}$
3. $\sqrt{\frac{QEL}{5m}}$
4. $\sqrt{\frac{4QEL}{5m}}$

Q.

A nucleus moving with a velocity $\overrightarrow{v}$ emits an $\alpha$-p article. Let the velocities of the $\alpha$-particle and the remaining nucleus be $\overrightarrow{v_1}$ and $\overrightarrow{v_2}$ and their masses be $m_1$, and $m_2$ respectively. Choose the correct option.

1. $\overrightarrow{v}$, $\overrightarrow{v_1}$ and $\overrightarrow{v_2}$ must be parallel to each other.

2. None of the two of $\overrightarrow{v}$, $\overrightarrow{v_1}$ and $\overrightarrow{v_2}$ should be parallel to each other.

3. $\overrightarrow{v_1}$ + $\overrightarrow{v_2}$ must be parallel to $\overrightarrow{v}$ .

4. $m_1\overrightarrow{v_1}+m_2\overrightarrow{v_2}$ must be parallel to $\overrightarrow{v}$ .

Q. Two blocks of masses 1 kg and 2 kg are suspended at the end of a light string passing over a frictionless pulley of mass 4 kg and radius 10 cm. When the masses are released, the acceleration of the masses is:

1. $\frac{g}{9}$
2. $\frac{g}{7}$
3. $\frac{g}{5}$
4. $\frac{g}{8}$

Q. Four particles of masses 'm', 'm', '2m' and '2m' are placed at the four corners of a square of side a as shown in diagram The (x, y) coordinates of the centre of mass are

1. $(\frac{a}{2},2a)$
   
2. $(\frac{a}{2},a)$
   
3. $(\frac{a}{2},\frac{2a}{3})$
   
4. $(a,\frac{a}{3})$