System of Particles and Rotational Motion Test

Result

System of Particles and Rotational Motion Test - 79

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Weekly Quiz Competition

Question 1
1 / -0

A disc of radius r rolls on without slipping on a rough horizontal floor. If velocity of its centre of mass is v then velocity of point p, as shown in the figure $$\left[ O P = \left( \cfrac { r } { 2 } \right) \text { and } \angle Q O P = 60 ^ { \circ } \right]$$ is-

A
$$\left( \cfrac { v _ { 0 } } { 2 } \right) \sqrt { 7 }$$

B
$$\left( \cfrac { v _ { 0 } } { 2 } \right) \sqrt { 3 }$$

C
$$\mathrm { v } _ { 0 }$$

D
$$\left( \cfrac { v _ { 0 } } { 2 } \right)$$

Solution
Question 2
1 / -0

Locate centre of mass of a uniform semicircular loop of radius R (shown in figure)

A
$$\frac{2 \ R}{\pi} \ above \ C_1$$

B
$$\frac{2 \ R}{2 + \pi}\ above \ C_1$$

C
$$\frac{R}{2 + \pi} \ above \ C_1$$

D
$$\frac{3 \ R}{2 + \pi} \ above \ C_1$$

Solution
Question 3
1 / -0

The maximum tension that an inextensible ring of radius 1m and mass density 0.1 $$kg\;{m^{ - 1}}$$ can bear is 40 N. The maximum angular velocity with which it can be rotated in a circular path is.

A
20 rad/s

B
18 rad/s

C
16 rad/s

D
15 rad/s

Solution
Question 4
1 / -0

A uniform disc of mass m and radius R is rotating with angular velocity $$ \omega $$ on a smooth horizontal surface. another identical disc is moving translationally with velocity v as shown.
when they touch each other, they stick together. the angular velocity of centre of mass of the system after contact will be

A
zero

B
$$ \dfrac {2v-R \omega }{6R} $$

C
$$ \dfrac {v}{R} $$

D
$$ \dfrac { \omega }{\sqrt(2)} $$

Solution
Question 5
1 / -0

A particle $$P$$ strikes the rod $$R$$ perpendicularly as shown. The rod is suspended vertically with upper end hinged $$\left( x = \dfrac { 1 } { 2 } , \text { elastic collision } \right)$$ Then select correct statement:

A
Linear momentum of $$P.R$$ system increases

B
Linear momentum of $$P.R$$ system decreases

C
Linear momentum of $$P.R$$ system remains constant

D
None of these

Solution
Question 6
1 / -0

A uniform thick plate in the shape of an arrow head has dimensions as shown in the given figure. The centre of mass lies at a point.

A
1.5 cm to the right of O

B
3 cm to the right of O

C
O itself

D
1 cm to the right of O

Solution
Question 7
1 / -0

A uniform circular disc of radius a is taken. A circular portion of radius b has been removed from it as shown in the centre of the disc, the distance $$x_2$$ of the centre of mass of the remaining part from the initial centre of mass O is given by:-

A
$$\frac{\pi b^2}{(a^2- b^2)}$$

B
$$\frac{-c b^2}{(a^2- b^2)}$$

C
$$\frac{\pi c^2}{(a^2- b^2)}$$

D
$$\frac{\pi a^2}{(c^2- b^2)}$$

Solution
Question 8
1 / -0

Two rods of equal mass m and length $$l$$ lie along the $$ x $$ axis and $$ y $$ axis with their centres at the origin.What is the moment of inertia of both about the line $$ x=y : $$

A
$$ \frac{m l^{2}}{3} $$

B
$$ \frac{m l^{2}}{4} $$

C
$$ \frac{m l^{2}}{12} $$

D
$$ \frac{m l^{2}}{6} $$

Solution
Question 9
1 / -0

Select correct statement regarding centrn of mass

A
In uniform symmetrical body it coincides with geometrical centre

B
It necessarily lies at centre of gravity

C
In center of mass frame momentum of system is zero

D
Both (1) & (3)

Solution
Question 10
1 / -0

A uniform metre rule of mass 100$$\mathrm { g }$$ is balanced on afulcrum at mark 40$$\mathrm { cm }$$ by suspending an unknownmass $$m$$ at the mark 20$$\mathrm { cm } .$$

A
Find the value of $$m$$

B
To which side the rule will tilt if the mass $$m$$ is
moved to the mark 10$$\mathrm { cm } ?$$

C
What is the resultant moment now?

D
How can it be balanced by another mass of
50$$\mathrm { g } ?$$

Solution