System of Particles and Rotational Motion Test

Result

System of Particles and Rotational Motion Test - 54

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Question 1
1 / -0

A thin wire of length l and uniform linear mass density p is bent in the form of a square. Its moment of inertia about an axis along one of its edge is

A
$$\frac{2p}{3} (\frac{l}{4})^3$$

B
$$\frac{3p}{2} (\frac{l}{4})^3$$

C
$$\frac{5p}{3} (\frac{l}{4})^3$$

D
$$\frac{1p}{3} (\frac{l}{4})^3$$
Question 2
1 / -0

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

A
Translatory

B
Oscillatory

C
SHM

D
All of these

Solution
Question 3
1 / -0

The moment of inertia of NaCl molecules with bond length r about an axis perpendicular to the bond and passing through the centre of mass is

A
$$({ m }_{ Na }+{ m }_{ Cl }){ r }^{ 2 }$$

B
$$\frac { { m }_{ Na }\times { m }_{ Cl } }{ { m }_{ Na }+{ m }_{ Cl } } { r }^{ 2 }$$

C
$$\frac { { m }_{ Na }+{ m }_{ Cl } }{ { m }_{ Na }\times { m }_{ Cl } } { r }^{ 2 }$$

D
$$\frac { { m }_{ Na }+{ m }_{ Cl } }{ { m }_{ Na }-{ m }_{ Cl } } { r }^{ 2 }$$

Solution
Question 4
1 / -0

Moment of inertia of a thin rod of length $$L$$ and mass $$M$$ about an axis passing through one of its end is

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

B
$$\dfrac {ML^{2}}{12}$$

C
$$\dfrac {ML^{2}}{2}$$

D
None of these

Solution
Question 5
1 / -0

If the linear momentum is increased by $$5$$% the kinetic energy will be increased by:

A
$$50$$%

B
$$100$$%

C
$$125$$%

D
$$10$$%

Solution
Question 6
1 / -0

A mass of 3 Kg has a velocity of $$\hat{i}$$ + 6$$\hat{j}$$ $$ms^{-1}$$. The momentum will be:

A
$$ \left( 3\hat { i } +18\hat { j } \right) ms^{-1} $$

B
$$ \left( 2.3\hat { i } -4.1\hat { j } \right) ms^{-1} $$

C
$$ \left( 3.2\hat { i } -4.1\hat { j } \right) ms^{-1} $$

D
$$ \left( 2.3\hat { i } +4.1\hat { j } \right) ms^{-1} $$

Solution
Question 7
1 / -0

Two particle of mass $$2$$ kg and $$4$$ kg move a linear path in opposite direction with velocity $$2ms^-1$$ and $$3ms^-1$$, then velocity of centre of mass of system is....

A
$$\frac{5}{3}m{s^{ - 1}}$$n the direction of second

B
$$\frac{4}{3}m{s^{ - 1}}$$n the direction of second

C
$$\frac{7}{3}m{s^{ - 1}}$$n the direction of second

D
$$\frac{8}{3}m{s^{ - 1}}$$ in the direction of second object
Question 8
1 / -0

A particle with linear momentum of magnitude P is subjected to a force F= Kt (k > 0) which is directed along the directed of initial momentum. The time which its liner momentum changes to 3P is :

A
$$\sqrt { \dfrac { 2P }{ K } } $$

B
$$2\sqrt { \dfrac { P }{ K } } $$

C
$$\sqrt { \dfrac { 2K }{ P } } $$

D
$$2\sqrt { \dfrac { K }{ P } } $$

Solution

Impulse is $$dP=Fdt$$
integrating both sides we get $$\int _{P}^{3P}dP=\int _{t=0}^{t}Ktdt$$
or $$2P=\dfrac{Kt^2}{2}$$ so $$t=\sqrt{\dfrac{4P}{K}}$$
Question 9
1 / -0

Two particles approach each other with different velocities. After collision , one of the particles momentum $$\overrightarrow { p } $$ in their center of mass frame. in the same frame, the momentum of the other particles.

A
0

B
$$-\overrightarrow { p } $$

C
$$-\overrightarrow { p } /2$$

D
$$-2\overrightarrow { p } $$

Solution

If there is no external force hence the momentum will be conserved in the frame of centre of mass so the momentum in the frame of reference is 0. As given if one's momentum after collision is p.
then the other one's momentum will be −p.
Question 10
1 / -0

The linear mass density $$\lambda ( x )$$ for a one dimensional rod of length $$x _ { 0 }$$ is plotted in the graph given below.The centre of mass lies at

A
$$ x _ { 0 }$$

B
$$\cfrac { 2 } { 3 } x _ { 0 }$$

C
$$\cfrac { x _ { 0 } } { 2 }$$

D
$$\cfrac { 3 } { 4 } x _ { 0 }$$

Solution