System of Particles and Rotational Motion Test

Result

System of Particles and Rotational Motion Test - 77

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Weekly Quiz Competition

Question 1
1 / -0

An insect of mass m is initially at rest at the one end of a stick length L and mass M, which rests on a smooth horizontal floor. The coefficient of friction between the insect and stick is k. The insect starts moving to reach the other end in shortest possible time. Choose the incorrect statement.

A
The centre of mass of the stick has speed $$v=\left[ \dfrac { kmg }{ 3M } \right] t$$ w.r.t. horizontal floor at time t

B
Time taken by the insect to reach the other end is $$t=\sqrt { \dfrac { 2LM }{ k(M+m)g } } $$

C
The magnitude of the linear momentum of the insect at time 't' is equal to kmgt

D
The maximum speed acquired by the stick is $${ v }_{ max }=\sqrt { \dfrac { 2kLM{ m }^{ 2 }g }{ (M+m)m } } $$
Question 2
1 / -0

The angular speed of a body changes from $$ \omega_1 $$ to $$ \omega_2 $$ without applying a torque but due to change in its moment of inertia.the ratio of radii of gyration in the two cases is

A
$$ \sqrt \omega_2 : \sqrt \omega_1 $$

B
$$ \sqrt \omega_1 : \sqrt \omega_2 $$

C
$$ \omega_1 : \omega_2 $$

D
$$ \omega_2 : \omega_1 $$

Solution
Question 3
1 / -0

A woman of mass m stands at the edge of a solid cylindrical platform of mass $$M$$ and radius $$R$$. At $$t=0$$ the platform is rotating with negligible friction at angular velocity $${ \omega }_{ 0 }$$ about a vertical axis passing through the centre. The woman begins to walk with speed v, relative to the platform, towards the center of the platform.

A
Angular velocity when woman reaches the centre is $$\left( v+\dfrac { m }{ M } \right) { \omega }_{ 0 }$$

B
Angular velocity as function of time is $$\omega =\dfrac { M+m }{ M+2m(1-vt/R)^{ 2 } } $$

C
Energy of system is conserved

D
Momentum of woman increases in magnitude

Solution

As the woman start moving towards the center of the platform the center of the mass of the whole system move towards the center of platform.

Hence, moment of inertia decreases as no external torque is being applied
the total angular momentum remains constant.

This results in increase of angular velocity.

Energy $$= 1/2 I \omega ^{2}$$

Here I decreases and omega increases.

So, energy remains constant,
Question 4
1 / -0

A body of mass $$m$$ moves in a circular path with uniform angular velocity. The motion of the body has constant

A
acceleration

B
velocity

C
monentum

D
kinetic energy

Solution
Question 5
1 / -0

A simple pendulum of mass $$m$$ executes $$SHM$$ with total energy $$E$$. If at an instant it is at one of extreme positions, then its linear momentum after a phase shift of $$\dfrac { \pi }{ 3 }\ rad$$ will be

A
$$\sqrt { 2mE } $$

B
$$ \dfrac { \sqrt{3mE} }{ 2 }$$

C
$$\sqrt { \dfrac { 2mE }{ 3 } } $$

D
$$2\sqrt { mE } $$

Solution
Question 6
1 / -0

Four masses are joined to a light circular frames in the figure. The radius of gyration of this system about an axis passing through the centre of the circular frame and perpendicular to its plane would be (where a is the radius of the circle)

A
$$\dfrac { a }{ \sqrt { 2 } } $$

B
$$\dfrac a 2$$

C
$$a$$

D
$$2a$$

Solution
Question 7
1 / -0

A child is standing at one end of long trolley moving with a speed V on a smooth horizontal track. If the child starts running towards the other end of the trolley with a speed u the centre of mass of the system(trolley +child) will move with a speed

A
$$(v-u)$$

B
$$v$$

C
$$(v+u)$$

D
$$zero$$

Solution

Zero.
The child is running arbitrarily on a trolley moving with velocity v. However, the running of the child will produce no effect on the velocity of the centre of mass of the trolley. This is because the force due to the boy's motion is purely internal. Internal forces produce no effect on the motion of the bodies on which they act.
Therefore no external force is involved in the boy—trolley system, the boy's motion will produce no change in the velocity of the centre of mass of the trolley.
Question 8
1 / -0

For a particle showing motion under the force $$F=-5{ \left( x-2 \right) },$$ the motion is

A
Translatory

B
Oscillatory

C
SHM

D
Both (2) & (3)

Solution
Question 9
1 / -0

$$1 J$$ of work is required to stop an iron rim from rolling on a horizontal floor.The mass and the radius of the rim are $$3 \text { kg and } 40 \mathrm { cm }$$ respectively. What is the speed of the centre of mass of the rim?

A
$$19 \mathrm { cm } / \mathrm { s }$$

B
$$27 \mathrm { cm } / \mathrm { s }$$

C
$$58 \mathrm { cm } / \mathrm { s }$$

D
$$89 \mathrm { cm } / \mathrm { s }$$
Question 10
1 / -0

In the figure shown $$ABC$$ is a uniform wire. If centre of mass of wire lies vertically below point $$A$$, then $$\cfrac{BC}{AB}$$ is close to:

A
$$1.85$$

B
$$1.37$$

C
$$1.5$$

D
$$3$$

Solution