CBSE Questions for Class 11 Engineering Physics Systems Of Particles And Rotational Motion Quiz 7 - MCQExams.com

In moment of inertia of a uniform rod of length $$'l'$$ and mass $$"m"$$ above an axis passing through one end of rod and inclined at angle $$\theta$$ to rod is:
  • $$\dfrac {ml^{2}}{3}\cos^{2}\theta$$
  • $$\dfrac {ml^{2}}{3}\sin^{2}\theta$$
  • $$\dfrac {ml^{2}}{12}\cos^{2}\theta$$
  • $$\dfrac {ml^{2}}{12}\sin^{2}\theta$$
A thin uniform circular ring is rolling down an inclined plane of inclination $$30^0$$ without slipping.Its linear acceleration along the inclined plane is
  • $$g$$
  • $$\dfrac{9}{2}$$
  • $$\dfrac{9}{3}$$
  • $$\dfrac{9}{4}$$
The block of mass $$m_{2}=10\ kg$$ is given a sharp impulse so that it acquires a velocity $$v_{0}=30\ m/s$$ towards right. Find the velocity of the centre of mass.($$m_{2}=5\ kg$$ and $$k=30\ N/m$$)
1081714_d5a17be6b5b04974824feecee19570a9.png
  • $$5\ m/s$$
  • $$10\ m/s$$
  • $$15\ m/s$$
  • $$20\ m/s$$
Moment of inertia of a uniform rod of length L and mass M, about an axis passing through L/4 from one end and perpendicular to its length is
  • $$\dfrac{7}{36} ML^2$$
  • $$\dfrac{7}{48} ML^2$$
  • $$\dfrac{11}{48} ML^2$$
  • $$\dfrac{ML^2}{12}$$
Two like parallel forces $$20\ N$$ and $$30\ N$$ act at the ends $$A$$ and $$B$$ of a rod $$1.5\ m$$ long. The resultant of the forces will act at the point:
  • $$90\ cm$$ from A
  • $$75\ cm$$ from B
  • $$20\ cm$$ from B
  • $$85\ cm$$ from A
Find out angular velocity of disc . If the disc is confined to roll without slipping at points of contact Radius of a disc is $$5$$ cm:-
  • $$\frac { 3v }{10} $$
  • $$\frac { 4v }{10} $$
  • $$\frac { 3v }{14} $$
  • $$\frac { 2v }{9} $$
The moment of inertia of a thin rod of length L and mass M about an axis passing through a point at a distance $$\dfrac{L}{3}$$ from one of its ends and perpendicular to the rod is :-
  • $$\dfrac{7}{48}ML^2$$
  • $$\dfrac{ML^2}{9}$$
  • $$\dfrac{ML^2}{12}$$
  • $$\dfrac{ML^2}{2}$$
The moment of inertia of a uniform rod of length $$2l$$ and mass $$m$$ about an axis $$xx'$$ passing through its centre and inclined at an angle $$\alpha $$ is
1093897_04298e5023c04151863ea8f15a15c0b8.PNG
  • $$\cfrac{ml^{2}}{3}\sin^{2}\alpha $$
  • $$\cfrac{ml^{2}}{12}\sin^{2}\alpha $$
  • $$\cfrac{ml^{2}}{6}\cos^{2}\alpha $$
  • $$\cfrac{ml^{2}}{2}\cos^{2}\alpha $$
$$Wb/m^{-2}$$ making an angle $$30^\circ$$ with the field. Find the couple acting on it.
  • $$2.5 \ Nm$$
  • $$5.5 \ Nm$$
  • $$7.5 \ Nm$$
  • $$9.0 \ Nm$$
A torque of $$2$$ newton$$-m$$ produced an angular acceleration of $$2\ rad/sec^{2}$$ a body. If its radius of gyration is $$2m$$, mass will be-
  • $$2\ kg$$
  • $$4\ kg$$
  • $$1/2\ kg$$
  • $$1/4\ kg$$
If linear mass density of a rod of length $$2$$m varies as $$\lambda =3x+2$$, then the position of the centre of gravity of the rod is?
  • $$1$$m
  • $$1.5$$m
  • $$1.2$$m
  • $$2$$m
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
  • $$1:3$$
  • $$3:1$$
  • $$\dfrac{1}{\sqrt [ 3 ]{ 9 } }$$
  • $$\sqrt [ 3 ]{ 9 } $$ 
A wheel having moment of inertia $$2\ kgm^{-2}$$ about its axis, rotates at $$50\ rpm$$ abut this axis. The angular retardation that can stop the wheel in one minute is
  • $$\dfrac {\pi}{36}rad\ s^{-2}$$
  • $$\dfrac {\pi}{18}rad\ s^{-2}$$
  • $$\dfrac {\pi}{72}rad\ s^{-2}$$
  • $$\dfrac {\pi}{9}rad\ s^{-2}$$
An object comprises of a uniform ring of radius $$R$$ and its uniform chord $$AB$$ (not necessarily made of same material) as shown in figure. Which of the following can be the centre of mass of the object.
1112162_572e0fa1653a4264a98609eb866829b0.PNG
  • $$\left(\dfrac{R}{3}, \dfrac{R}{3}\right)$$
  • $$\left(\dfrac{R}{2}, \dfrac{R}{2}\right)$$
  • $$\left(\dfrac{R}{4}, \dfrac{R}{4}\right)$$
  • $$\left(\dfrac{R}{\sqrt{2}}, \dfrac{R}{\sqrt{2}}\right)$$
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?
  • $$\dfrac{1}{3} Ml^2$$
  • $$\dfrac{8}{3} Ml^2$$
  • $$\dfrac{2}{3} Ml^2$$
  • $$\dfrac{13}{3} Ml^2$$
The moment of inertia of a thin uniform rod of mass $$M$$ and length $$L$$ about an axis perpendicular to its length is $$\dfrac{ML^{2}}{g}$$. The distance of the axis from the centre of the rod is:-
  • $$\dfrac{L}{3}$$
  • $$\dfrac{L}{6}$$
  • $$\dfrac{L}{4}$$
  • $$\dfrac{L}{2}$$
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 :
  • $$\dfrac{2}{3} mL^2$$
  • $$\dfrac{mL^2}{6}$$
  • $$\dfrac{3 mL^2}{4}$$
  • $$\dfrac{4 mL^2}{3}$$
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
  • $$\cfrac { 3AL+2{ BL }^{ 2 } }{ 3(2A+BL) } $$
  • $$\cfrac { 2AL+2{ BL }^{ 2 } }{ 3(2A+BL) } $$
  • $$\cfrac { AL+2{ BL }^{ 2 } }{ (2A+BL) } $$
  • $$\cfrac { 3AL+2{ BL }^{ 2 } }{(2A+BL) } $$
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
  • $$\cfrac{2}{3}M{l}^{2}$$
  • $$\cfrac{13}{3}M{l}^{2}$$
  • $$\cfrac{1}{3}M{l}^{2}$$
  • $$\cfrac{4}{3}M{l}^{2}$$
Two point like spheres of mass $$5\ kg$$ are joined by $$1m$$ long weightless rod. The $$M.I.$$ in $$kg$$. $$m^{2}$$ unit about an axis perpendicular to the rod and through the center of any of the sphere will be (in kg-$$m^{2})$$-
  • 10
  • 2.5
  • 5.0
  • 1.0
Two spheres of masses $$4kg$$ and $$8kg$$ are moving with velocities $$2{ms}^{-1}$$ and $$3{ms}^{-1}$$ away from each other along the same line. The velocity of centre of mass is
  • $$\cfrac{8}{3}{ms}^{-1}$$ towards second sphere
  • $$\cfrac{8}{3}{ms}^{-1}$$ towards first sphere
  • $$\cfrac{4}{3}{ms}^{-1}$$ towards second sphere
  • $$\cfrac{4}{3}{ms}^{-1}$$ towards first sphere
A spherical body of radius $$'R'$$ rolls on a horizontal surface with linear velocity $$'v'$$. Let $$L_1$$ and $$L_2$$ be the magnitudes of angular momenta of the body about centre of mass and point of contact $$P$$. Then,
  • $$L_2 = 2 L_1$$; if radius of gyration $$K = R$$
  • $$L_2 = 2 L_1$$; for all cases
  • $$L_2 > 2 L_1$$; if radius of gyration $$K < R$$
  • None of these
A particle is moving along a straight line parallel to x-axis with constant  velocity . Find angular momentum about the origin in vector form
1119528_7568f92e8f9e469bb75522d27b3bd72b.png
  • $$ + m{v^2}b\hat k$$
  • $$ mb\hat k$$
  • $$  2mvb\hat k$$
  • $$  mvb\hat k$$
The mass per unit length of a non-uniform rod of length $$L$$ varies as $$m = \lambda x$$ where $$\lambda$$ is constant. The centre of mass of the rod will be at :
  • $$\dfrac{2}{3}L$$
  • $$\dfrac{3}{2}L$$
  • $$\dfrac{1}{2}L$$
  • $$\dfrac{4}{3}L$$
A shell fired from a gun at an angle to the horizontal explodes in mid air. Then the centre of mass of the shell fragments will move
  • vertically down
  • horizontally
  • along the same parabolic path along which the 'intact' shell was moving
  • along the tangent to the parabolic path of the 'intact' shell, at the point of explosion.
Force-time graph for the motion of a body is shown in figure. Change is linear momentum between 0 s to 8 s is : 
1127558_49a4e5615b8d4867be389ad86b21333d.png
  • Zero
  • 4 N-s
  • 8 N-s
  • None of the above
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 
  • $$30\ m/s$$
  • $$20\ m/s$$
  • $$10\ m/s$$
  • $$5\ m/s$$
The moment of inertia of a uniform rod of length $$2l$$ and mass '$$m$$' about an axis through centre and inclined at an angle $$\theta $$ to rod is:
  • $$\dfrac{ml^2}{3}\sin^2\theta$$
  • $$\dfrac{ml^2}{6}\cos^2\theta$$
  • $$\dfrac{ml^2}{2}\cos^2\theta$$
  • $$\dfrac{ml^2}{12}\cos^2\theta$$
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 $$0.2 m$$)
  • $$2.5 \ rev/s$$
  • $$1.25 \ rev/s$$
  • $$5 \ rev/s$$
  • None of these
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
  • increases
  • decreases
  • remains unchanged
  • doubles

Two persons A and B of weight 80 kg and 50 kg respectively are standing at opposite ends of a boat of mass 70 kg and length 2m, at rest. When they interchange their positions then the displacement of the center of mass of the boat will be


1133202_180c85633ace4eb7a13fb2f2232ed76e.png
  • 60 cm towards left
  • 30 cm towards right
  • 30 cm towards left
  • stationary
A wire of length $$l$$ and mass $$m$$ is bent in the form of a rectangle $$ABCD$$ with $$\dfrac {AB}{BC}=2$$ . The moment of inertia of this wire frame about the side $$BC$$ is:
  • $$\dfrac {11}{252}ml^{2}$$
  • $$\dfrac {8}{203}ml^{2}$$
  • $$\dfrac {5}{136}ml^{2}$$
  • $$\dfrac {7}{162}ml^{2}$$
The radius of gyration of a uniform rod of length $$l$$ and mass $$M$$ about an axis passing through its centre and perpendicular to its length is:
  • $$\dfrac{l^2}{12}$$
  • $$\dfrac{l}{2\sqrt{3}}$$
  • $$\dfrac{l}{2}$$
  • $$\dfrac{l}{\sqrt{2}}$$
Two objects masses 200 g and 500 g posses velocities $$10i ms^{-1}$$ and $$3i + 5 j ms^{-1}$$ respectively. The velocity of their centre of mass $$ms^{-1}$$ is 
  • $$5 i - 25 j$$
  • $$\dfrac{5}{7} i - 25 j$$
  • $$5 i + \dfrac{25}{7} j$$
  • $$25 i - \dfrac{5}{7} j$$
If momenta of two particles of a system are given by $$\overrightarrow { { p }_{ 1 } } =2\hat { i } -\hat { j } +3\hat { k } $$ and $$\overrightarrow { { p }_{ 2 } } =$$ $$-\hat { i } +2\hat { j } +3\hat { k } $$, then the angle made by the direction of motion of the system with $$x$$-axis is 
  • $$\cos ^{ -1 }{ 1 } $$
  • $$\cos ^{ -1 }{ \sqrt { 36/38 } } $$
  • $$45^0$$
  • $$\cos ^{ -1 }{ \sqrt { 1/38 } } $$
A $$2$$ kg body and a $$3$$ kg body are moving along the x-axis. At a particular instant the $$2$$ kg body has a velocity of $$3$$ m/s and the $$3$$ kg body has the velocity of $$2$$ m/s. The velocity of the centre of mass at that instant is
  • $$5$$ m/s
  • $$1$$ m/s
  • Zero
  • $$2.4$$ m/s
Two bodies of 6 kg and 4 kg masses have their velocities $$5\hat{i} -2\hat{j} +10\hat{k}$$ and $$10\hat{i} -2\hat{j} +5\hat{k}$$ respectively. Then the velocity of their centre of mass is
  • $$5\hat{i}+2\hat{j}-8\hat{k}$$
  • $$7\hat{i}+2\hat{j}-8\hat{k}$$
  • $$7\hat{i}-2\hat{j}+8\hat{k}$$
  • $$7\hat{i}+2\hat{j}+8\hat{k}$$
A T joint is formed by two identical rods A and B each of mass m and length L in the X -Y plane as shown. Its moment of inertia about axis coinciding with A is 
1162477_aa4ad0f345b641daa5d0b2dabf78e5cd.jpg
  • $$\frac{2mL^2}{3}$$
  • $$\frac{mL^2}{12}$$
  • $$\frac{mL^2}{6}$$
  • None of these
Two particles of equal mass are moving along the same straight line with the same speed in opposite direction. What is the speed of the centre of mass of the system?
  • $$\dfrac{v}{2}$$
  • $$2v$$
  • $$v$$
  • $$0$$
In free space, a shell moving with velocity 60 m/s along the positive x-axis of an inertial frame, when passes the origin, explodes into two pieces of masses ratio 1 :Velocity of the mass center after the explosion is
  • 20 m/s
  • 60 m/s
  • 90 m/s
  • None of the above
Mass of thin long metal rod is $$2$$ kg and its moment of inertia about an axis perpendicular to the length of the rod and passing through its one end is $$0.5kg{m^2}$$. Its radius of gyration is:
  • $$25$$ cm
  • $$40$$ cm
  • $$50$$ cm
  • $$1$$ m
The linear density of a thin rod of length $$1.0$$m varies as $$\lambda =2$$kg/m$$+\left(\dfrac{2kg}{m^2}\right)x$$, where x is the distance from its one end. The distance of its centre of mass from its end is?
  • $$\dfrac{2}{3}$$m
  • $$\dfrac{5}{9}$$m
  • $$\dfrac{4}{3}$$m
  • $$\dfrac{1}{2}$$m
Three identical uniform rods each of length $$1cm$$ and Mass $$2kg$$ are arranged to form an equilateral triangle what is the moment of inertia of the system about an axis passing through one corner ans perpendicular to the plane of the triangle? 
  • $$4kg-m^2$$
  • $$3kg-m^2$$
  • $$2kg-m^2$$
  • None of these
Moment of a inertia of a sphere about its diameter is $$2/5\ MR^{2}$$. What  its moment of inertia about an axis perpendicular to its two diameter and passing through their point of intersection.?
  • $$I=\dfrac{2}{5}Mr^{2}$$
  • $$I=\dfrac{3}{5}Mr^{2}$$
  • $$I=\dfrac{4}{5}Mr^{2}$$
  • $$I=\dfrac{5}{5}Mr^{2}$$
The wheel of radius $$r= 300 mm$$ rolls to the right without slipping and has a velocity $$v_0= 3 m/s$$ of its center O. The speed of the point A on the wheel for the instant represented in the figure is:-
1164266_c485dca6b7084c378e3ba9e65368d2e3.png
  • $$4.36 $$ m/s
  • $$5 $$ m/s
  • $$3 $$ m/s
  • $$1.5$$ m/s
Find the M.I of rod about (i) an axis perpendicular to the rod and passing through left end (ii)An axis through its centre of mass and perpendicular to the length whose linear density varies as $$\lambda=ax$$ where a is a positive constant and $$'x'$$ is the position of an element of the rod relative to its left end.The length of the rod is $$l$$
  • $$\dfrac{al^4}{4}$$
  • $$\dfrac{al^3}{4}$$
  • $$\dfrac{al^4}{2}$$
  • $$\dfrac{al^3}{6}$$
Find the torque of a force $$\vec{F}=-3\hat{i}+\hat{j}+5 \hat{k}$$ acting at the point $$\vec{r}=7\hat{i}+3\hat{j}+\hat{k}$$ with respect to origin:-
  • $$14 \hat{i}-32 \hat{j}-2 \hat{k}$$
  • $$4 \hat{i}+4 \hat{j}+6 \hat{k}$$
  • $$-14 \hat{i}+38 \hat{j}-16 \hat{k}$$
  • $$-21\hat{i}+3 \hat{j}+5\hat{k}$$

Four uniform thin rods each of mass 1 kg and length 1 m are joined in the form of a square. If the square is rotated about axis AB, then it moment of inertia is 


1162825_e5e93ee8cbc441fab25a132b870ae57c.png
  • $$\frac{5}{3}{\text{kg}}\;{{\text{m}}^{\text{2}}}$$
  • $$\frac{3}{4}{\text{kg}}\;{{\text{m}}^{\text{2}}}$$
  • $$\frac{5}{4}{\text{kg}}\;{{\text{m}}^{\text{2}}}$$
  • $$\frac{7}{4}{\text{kg}}\;{{\text{m}}^{\text{2}}}$$
A bullet of mass m is fired at a certain angle $$\theta$$b with the horizontal. The bullet returns to ground after time t. Then the change in momentum of the bullet is 
  • zero
  • $$ 2mu sin \theta$$
  • $$\dfrac{mgt cos \theta}{2}$$
  • mgt
A circular disc of M.I. 10 $$kg-m^2$$ rotates about its own axis at a constant speed of 60 r.p.m. under the action of an electric motor of power 31.4 W. If the motor is switched off, how many rotations will it cover before coming to rest?
  • $$3.14$$
  • $$31.4$$
  • $$314$$
  • $$6.28$$
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