System of Particles and Rotational Motion Test

Result

System of Particles and Rotational Motion Test - 46

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Four identical thin rods each of mass $$M$$ and length $$l$$, form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is

A
$$\cfrac{2}{3}M{l}^{2}$$

B
$$\cfrac{13}{3}M{l}^{2}$$

C
$$\cfrac{1}{3}M{l}^{2}$$

D
$$\cfrac{4}{3}M{l}^{2}$$

Solution
Question 2
1 / -0

Two discs of same mass and same thickness have densities as $$17\ g/{cm}^{3}$$ and $$51\ g/{cm}^{3}$$. The ratio of their moment of inertia are in the ratio

A
$$1:3$$

B
$$3:1$$

C
$$\dfrac{1}{\sqrt [ 3 ]{ 9 } }$$

D
$$\sqrt [ 3 ]{ 9 } $$

Solution

$$I=\dfrac{1}{2}M{R}^{2}$$ ......$$(1)$$
Now, $$M=\dfrac{4}{3}\pi{R}^{3}d\rho$$ where $$m$$ is the mass, $$d$$ is the thickness and $$\rho$$ is the density
$$\Rightarrow R={\left(\dfrac{3M}{4\pi d\rho}\right)}^{\frac{1}{3}}$$
$$\Rightarrow {R}^{2}={\left(\dfrac{3M}{4\pi d\rho}\right)}^{\frac{2}{3}}$$
Hence eqn$$(1)$$ becomes,
$$I=\dfrac{1}{2}M\times {\left(\dfrac{3M}{4\pi d\rho}\right)}^{\frac{2}{3}}$$ .......$$(2)$$
Now if $$M$$ and $$d$$ are remaining constant as per the given condition then
$$I\propto\dfrac{I}{{\rho}^{\frac{2}{3}}}$$ ......$$(3)$$
Given: moment of inertia of first disk of density $${\rho}_{1}=17$$g/$${cm}^{3}$$ and
moment of inertia of second disk of density $${\rho}_{2}=51$$g/$${cm}^{3}$$
$$\dfrac{{I}_{1}}{{I}_{2}}={\left(\dfrac{{\rho}_{2}}{{\rho}_{1}}\right)}^{\frac{2}{3}}$$
$$={\left(\dfrac{51}{17}\right)}^{\frac{2}{3}}$$
$$={\left(\dfrac{3}{1}\right)}^{\frac{2}{3}}$$
$$={9}^{\frac{1}{3}}$$
Question 3
1 / -0

Four thin uniform rods of length $$L$$ and mass $$m$$ are joined to form a square. The moment of inertia of square about an axis along its one diagonal is :

A
$$\dfrac{2}{3} mL^2$$

B
$$\dfrac{mL^2}{6}$$

C
$$\dfrac{3 mL^2}{4}$$

D
$$\dfrac{4 mL^2}{3}$$

Solution

From Perpendicular axis theorem
$$I_z=I_y +I_x\quad \left\{I_x =I_y \right\}$$
$$\boxed {I_z =2I_x}$$

from parallel axis theorem $$I_z =I_{com}+md^2$$

$$\Rightarrow \ I_z=\dfrac {ML^2}{12}+M\left (\dfrac {L}{2}\right)^2$$

$$\Rightarrow \ I_z =\dfrac {ML^2}{12}+\dfrac {ML^2}{4}\ \Rightarrow \boxed {I_z =\dfrac {1}{3} ML^2}\to$$ For single Ros

for $$4$$ rod $$I_z =4\times \dfrac {1}{3} ML^2 =\dfrac {4}{3}ML^2$$

$$\boxed {I_x =\dfrac {I_z}{2}=\dfrac {\dfrac {4}{3}ML^2}{2}=\dfrac {2}{3}ML^2}$$
Question 4
1 / -0

A wire of length $$L$$ and mass $$M$$ is bent in the form of a circular ring. Its moment of inertia about its axis is

A
$$4\pi ML^{2}$$

B
$$\dfrac {ML^{2}}{8\pi^{2}}$$

C
$$8\pi^{2} ML^{2}$$

D
$$\dfrac {ML^{2}}{4\pi^{2}}$$

Solution
Question 5
1 / -0

Force-time graph for the motion of a body is shown in figure. Change is linear momentum between 0 s to 8 s is :

A
Zero

B
4 N-s

C
8 N-s

D
None of the above

Solution
Question 6
1 / -0

Two blocks of masses $$10\ kg$$ and $$4\ kg$$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $$14\ m/s $$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is

A
$$30\ m/s$$

B
$$20\ m/s$$

C
$$10\ m/s$$

D
$$5\ m/s$$

Solution
Question 7
1 / -0

The linear density of a rod of length $$L$$ varies as $$\rho=A+Bx$$ where $$x$$ is the distance from the left end. The distance of centre of mass from $$O$$ is

A
$$\cfrac { 3AL+2{ BL }^{ 2 } }{ 3(2A+BL) } $$

B
$$\cfrac { 2AL+2{ BL }^{ 2 } }{ 3(2A+BL) } $$

C
$$\cfrac { AL+2{ BL }^{ 2 } }{ (2A+BL) } $$

D
$$\cfrac { 3AL+2{ BL }^{ 2 } }{(2A+BL) } $$

Solution
Question 8
1 / -0

A man stands at the centre of a turn table it extended horizontally, with a $$5 kg$$ mass hand. He is set into rotation with an angular of one revolution in $$2s$$. His new angular is he drops his hands to his sides is (Assume moment of inertia of the man is $$6 \ kgm^2$$. The distance of the wavelength from the axis is $$1 m$$and final distance is $$0.2 m$$)

A
$$2.5 \ rev/s$$

B
$$1.25 \ rev/s$$

C
$$5 \ rev/s$$

D
None of these
Question 9
1 / -0

Three particles each of mass $$200 g$$, are kept at corners of an equilateral triangle of side $$10 cm$$. Find the moment of inertia of the system about an axis joining two of the particle.

A
$$0.5 \times {10^{ - 3}}\,kg - {m^2}$$

B
$$4.5 \times {10^{ - 3}}\,kg - {m^2}$$

C
$$1.5 \times {10^{ - 3}}\,kg - {m^2}$$

D
$$2.5 \times {10^{ - 3}}\,kg - {m^2}$$
Question 10
1 / -0

A person sitting firmly over a rotating stool has his arms stretched. If he folds his arms, his angular momentum about the axis of rotation

A
increases

B
decreases

C
remains unchanged

D
doubles

Solution