Why Com Is an Important Point

Q. Calculate the reduced mass of $HCl$ molecule.
Given that the mass of $H$ atom is $1.0078\text{amu}$ and the mass of Cl atom is $34.9688\text{amu}$.
Note that $1\text{amu}=1.660565\times {10}^{-27}\text{kg}$.

1. $1.627\times {10}^{-27}\text{kg}$
2. $2.538\times {10}^{-27}\text{kg}$
3. $1.253\times {10}^{-27}\text{kg}$
4. $1.978\times {10}^{-27}\text{kg}$

Q. Which of the following statements are correct?
a) Centre of mass of a body always coincides with the centre of gravity of the body.
b) Centre of mass of a body is the point at which the total gravitational torque on the body is zero.
c) A couple on a body produce both translational and rotation motion in a body.
d) Mechanical advantage greater than one means that small effort can be used to lift a large load.

1. (a) and (b)
2. (b) and (c)
3. (c) and (d)
4. (b) and (d)

Q. Two blocks of masses $3\text{kg}$and $6\text{kg}$ respectively are placed on a smooth horizontal surface. They are connected by a light spring of force constant $k=200\text{N/m}$. Initially the spring is unstretched. The indicated velocities are imparted to the blocks. Find the maximum extension of the spring.

1. $15\text{cm}$
2. $90\text{cm}$
3. $30\text{cm}$
4. $60\text{cm}$

Q. A stone of mass $1\text{kg}$ is tied with a string, and it is whirled in a vertical circle of radius $1\text{m}$. If tension at the highest point is $14\text{N}$, then velocity at the lowest point will be
$($Take value of $g=10{\text{m/s}}^2)$

1. $3\text{m/s}$
2. $4\text{m/s}$
3. $6\text{m/s}$
4. $8\text{m/s}$

Q. Two objects are moving on a surface.The center of mass exists only if -

1. the two objects are physically connected
2. the surface is level
3. the surface is frictionless
4. There is always a center of mass.

Q. The reduced mass of two particles having masses $4m$ and $2m$ is

1. $2m$
2. $3m$
3. $\frac{4m}{3}$
4. $\frac{m}{2}$

Q. Which of the following statements are correct?
a) Centre of mass of a body always coincides with the centre of gravity of the body.
b) Centre of mass of a body is the point at which the total gravitational torque on the body is zero.
c) A couple on a body produce both translational and rotation motion in a body.
d) Mechanical advantage greater than one means that small effort can be used to lift a large load.

1. (a) and (b)
2. (b) and (c)
3. (c) and (d)
4. (b) and (d)

Q. A moving body of mass m makes a head on elastic collision with another body of mass $2$m which is initially at rest. Find the fraction of kinetic energy lost by the colliding particle after collision.

Q. The reduced mass of two particles having masses $m$ and $2m$ is

1. $2m$
2. $3m$
3. $\frac{2m}{3}$
4. $\frac{m}{2}$

Q.

Tell me distance which is not equal to zero if a man is falling with initial velocity zero and his final velociy as zero so that he does getsany hurt

And is it possible that if a man can have his final velocity as zero(suppose) that he will definitely don't gets any hurt

Q. Two blocks $A$ and $B$ of masses $2kg$ and $4kg$ are connected by a light spring of force constant $4800N/m$ . The system is at rest on a smooth horizontal surface with the spring in its natural state without any compression or extension. Now a velocity of $6m/s$ is given to B in a direction away from $A$. During the subsequent motion, the maximum extension of the spring is:

1. $5cm$
2. $10cm$
3. $15cm$
4. $20cm$

Q. Two blocks of masses $3\text{kg}$and $6\text{kg}$ respectively are placed on a smooth horizontal surface. They are connected by a light spring of force constant $k=200\text{N/m}$. Initially the spring is unstretched. The indicated velocities are imparted to the blocks. Find the maximum extension of the spring.

1. $30\text{cm}$
2. $60\text{cm}$
3. $15\text{cm}$
4. $90\text{cm}$

Q. A block of mass $m$, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant $k$. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force $F$, the maximum speed of the block is:

1. $\frac{\pi F}{\sqrt{mk}}$
2. $\frac{F}{\sqrt{mk}}$
3. $\frac{F}{\pi \sqrt{mk}}$
4. $\frac{2F}{\sqrt{mk}}$

Q. Masses of 1 kg, 2 kg and 3 kg are placed at the corners of an equilateral triangle of side 1m. The magnitude of the gravitational force exerted by 2 kg and 3 kg masses on the 1 kg mass is

1. $\sqrt{17}G$
2. $\sqrt{15}G$
3. $\sqrt{19}G$
4. $\sqrt{13}G$

Q. The reduced mass of two particles having masses $4m$ and $2m$ is

1. $2m$
2. $3m$
3. $\frac{4m}{3}$
4. $\frac{m}{2}$

Q. A block \(B\) is attached to two unstretched springs \(S_1\) and \(S_2\) with spring constants \(k\) and \(4k\) respectively (see the figure I). The other ends are attached to the identical supports \(M_1\) and \(M_2\) which are not fixed to the walls. The springs and supports have negligible masses. There is no friction anywhere. The block \(B\) is displaced towards the wall \(1\) by a small distance \(x\) (see the figure II) and then released. The block returns and moves a maximum distance \(y\) towards the wall \(2\). The displacements \(x\) and \(y\) are measured with respect to the equilibrium position of the block \(B\). The ratio \(\dfrac{y}{x}\) is


\( \begin{array}{l} \underset{y}{*} \mid \\ \end{array} \) I

Q. A uniform sphere is placed on a smooth horizontal surface and a horizontal force F is applied on it at a distance h above the surface. The acceleration of the center

1. is independent of h.
2. Is Maximum when h=0
3. is maximum when h=2R
4. is maximum when h=R

Q. A block of mass 1 kg moving with a speed of $2{ms}^{-1}$ collides with and sticks to another block of mass 2 kg which was initially at rest. After the collision

1. The momentum of the system is less than $2{kgms}^{-1}$
2. The kinetic energy of the system is $\frac{2}{3}J$
3. The kinetic energy of the system is $2J$
4. None of these

Q. A body having it's center of mass at the origin. Then,

1. x co-ordinates of the particles may be all positive.
2. total KE must be conserved.
3. total KE must very.
4. total momentum shall vary.

Q. A block of mass $m$ moving with a velocity ${\nu }_0$ collides with a stationary block of mass $M$ to which a spring of stiffness $k$ is attached, as shown in Fig. Choose the correct alternative.

1. The velocity of the centre of mass is ${\nu }_0$
2. The initial kinetic energy of the system in the centre of mass frame is $\frac{1}{4}\left(\frac{mM}{M+m}\right){\nu }_0^2$.
3. The maximum compression in the spring is ${\nu }_0\sqrt{\left(\frac{mM}{m+M}\frac{1}{k}\right)}$
4. When the spring is in the state of maximum compression, the kinetic energy in the centre of mass frame is zero.

Q. A uniform rod of mass m and length l is fixed from point A, which is at a distance l/4 from one end as shown in the fig. The rod is free to rotate in a vertical plane. The rod is released from the horizontal position.
What is the reaction at the hinge, when kinetic energy of the rod is maximum?

1. $\frac{13}{7}mg$
2. $\frac{5}{7}mg$
3. $\frac{11}{7}mg$
4. $\frac{4}{7}$

Q. Seven identical geese are flying south together at constant speed. A hunter shoots one of them, which immediately dies and falls to the ground. The other six continue flying south at the original speed. After the one goose has hit the ground, the center of mass of all seven geese

1. Stops with the dead goose.
2. Continues south, but at $\frac{6}{7}$ the original speed.
3. Continues south, but at $\frac{1}{7}$ the original speed.
4. Continues south at the original speed, but is now located some distance behind the flying geese.

Q. If the mass of a planet is 10% less than that of the earth and the radius is 20% greater than that of the earth, the acceleration due to gravity on the plant will be

1. 5/8 times on the surface of the earth
2. 3/4 times that on the surface of the earth
3. 1/2 times that on the surface of the earth
4. 9/10 times that on the surface of the earth

Q. A stone of mass $mkg$ is whirled in a verticle circle of radius $20cm$. The difference in kinetic energies at the lowest and the topmost position is

1. $4mgJ$
2. none of these
3. $0.4mgJ$
4. $40mgJ$

Q. If we suspend lamina at different positions, its center of gravity will still lie along the :

1. plumb line
2. line of weight
3. line of force
4. gravity line

Q. Two blocks of mass 3 kg and 6 kg respectively are placed on a smooth horizontal surface. They are connected by a light spring of force constant k=200Nm−1k=200Nm−1 are imparted in opposite directions to the respective blocks as shown in figure. The maximum extension of the spring will be

1. $15cm$
2. $20cm$
3. $25cm$
4. $30cm$

Q. Assertion :In the system shown in figure spring is first stretched the left to oscillate. At some instant kinetic energy of mass is $K$. At the same instant kinetic energy of mass 2m should be $\frac{K}{2}$. Reason: Their linear momenta are equal and opposite and $K=\frac{p^2}{2m}$ or $K\propto \frac{1}{m}$.

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. A force $F=-10x+2$ acts on a particle of mass $0.1$kg, where '$k$' is in m and $F$ in newton.If it is released from rest at $x=-2$m, find:(a) amplitude; (b) time period; (c) equation of motion.

1. (a)$\frac{11}{5}m$ (b)$\frac{\pi }{5}sec$ (c) $x=0.2-\frac{11}{5}cos\omega t$
2. (a)$\frac{11}{3}m$ (b)$\frac{\pi }{5}sec$ (c) $x=0.2-\frac{11}{5}cos\omega t$
3. (a)$\frac{11}{5}m$ (b)$\frac{\pi }{3}sec$ (c) $x=0.2-\frac{11}{5}cos\omega t$
4. (a)$\frac{11}{5}m$ (b)$\frac{\pi }{5}sec$ (c) $x=0.2-\frac{11}{3}cos\omega t$

Q. A particle is dropped from rest from a large height. Assume g to be constant throughout the motion. The time taken by it to fall through successive distance of 1 m each will be

1. In the ratio of the difference in the square roots of the integers,
   $\sqrt{1},(\sqrt{2}-\sqrt{1}),(\sqrt{3}-\sqrt{2}),(\sqrt{4}-\sqrt{3}),.....$
2. In the ratio of the reciprocals of the square roots of the integers, i.e., $\frac{1}{\sqrt{1}},\frac{1}{\sqrt{2}},\frac{1}{\sqrt{3}},....$
3. All equal, being equal to $\sqrt{2/g}$ second
4. In the ratio of the square roots of the integers 1, 2, 3, ...

Q. Two particles of mass $6\text{kg}$ and $24\text{kg}$ are separated by a certain distance. The ratio of distance of COM from $6\text{kg}$ mass and that from $24\text{kg}$ mass will be

1. $3:1$
2. $4:1$
3. $1:5$
4. $2:1$