CBSE Questions for Class 11 Engineering Physics Systems Of Particles And Rotational Motion Quiz 15 - MCQExams.com

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.
  • 20 rad/s
  • 18 rad/s
  • 16 rad/s
  • 15 rad/s
A 1 m long rod has mass of $$  o.12 kg $$ what is the moment of inertia about an axis passing through the centre and perpendicular to the length of rod 
  • $$0.01kg-{ m }^{ 2 }$$
  • $$0.001 kg-{ m }^{ 2 }$$
  • $$1 kg-{ m }^{ 2 }$$
  • $$10 kg-{ m }^{ 2 } $$
If a disc of mass $$m$$ and radius $$r$$ is reshaped into a ring of radius $$2$$ $$r$$ , the mass remaining the same, the radius of gyration about centroidal axis perpendicular to plane goes up by a factor of
  • $$\sqrt { 2 }$$
  • $$2$$
  • $$2$$$$\sqrt { 2 }$$
  • $$4$$
An electric fan has blades of length $$30 cm$$ measured from the axis of rotation. If the fan is running at $$120 rpm$$, the acceleration of a point on the tip of the blade is
  • $$1600 ms^{ -2 }$$
  • $$47.4 ms^{ -2 }$$
  • $$23.7 ms^{ -2 }$$
  • $$50.5 ms^{ -2 }$$
Mass of thin long metal rod is 2 kg and its moment of inertia about an axis perpendicular to the length of rod and passing through its one end is $$0.5 kgm^2$$. Its radius of gyration is 
  • 20 cm
  • 40 cm
  • 50 cm
  • 1 m
A rod of length 0.3 m having variable liner mass density from A to B as $$\lambda =\quad { \lambda  }_{ 0 }X$$ (X is distance from A in meter), where $${ \lambda  }_{ 0 }=100\quad kg/{ m }^{ 2 }$$ is suspended by two light wires of same length. Ratio of their linear mass density is 2:Then which of the following is/are correct:
1459081_85195ed600c448f5b4dfa97dec6e6b4b.png
  • Ratio of wave speed in wire -1 to wire-2 is 3:2
  • Ratio of wave speed in wire -1 to wire-2 is 3:1
  • Second harmonic in wire-1 has same frequency as third harmonic in wire-2
  • Third overtone in wire-1 has frequency as fifth overtone in wire
Two bodies of masses 2 kg and 4 kg are moving with velocities 2 m/s and 1 m/s towards each other due to mutual gravitational attraction. What is the velocity of their centre of mass ?
  • 5.3 m/s
  • 6 m/s
  • Zero
  • 8.1 m/s
An arrow sign is made by cutting and rejoining a quarter part of a square plate of side 'L' shown. The distance OC, where 'C' is the centre of mass of the arrow, is
1448772_7a16a535df9540da9a17d2a7ac665c1f.png
  • $$\dfrac { L }{ 3 } $$
  • $$\dfrac { L }{ 4 } $$
  • $$\dfrac { 3L }{ 8 } $$
  • None of these
If the linear density of a rod of length L varies as $$\lambda =A+B_x$$, compute its centre of mass.
  • $$[\cfrac {L(3A+2BL)}{3(2A+BL},0,0]$$
  • $$[0,\cfrac {(3A+2B)L}{(2A+3L},\cfrac L 2]$$
  • $$[0,0\cfrac {L(3A+2BL)}{3(2A+BL}]$$
  • $$[\cfrac L 2,00]$$
Find out the position of centre of mass of the figure shown below.
1441045_fb7351caffd7480bb027a1b3743e2c0b.jpg
  • $$r _ { 1 } = \frac { R ( 3 \pi + 4 ) } { 3 ( \pi + 8 ) }$$
  • $$r _ { 1 } = \frac { ( 3 \pi + 4 ) } { 3 ( \pi + 8 ) }$$
  • $$r _ { 1 } = \frac { \pi R ( 3 \pi + 4 ) } { 3 ( \pi + 8 ) }$$
  • $$r _ { 1 } = \frac { \pi ( 3 \pi + 4 ) } { 3 ( \pi + 8 ) }$$
A ladder PQ of length 5m inclined to a vertical wall is slipping over a horizontal surface with a velocity of $$2 ms^{-1}$$, when Q is at a distance 3 M from the ground. Calculate the velocity of centre of mass of the rod at this moment.
1446531_648adc16515a4f2f901ede81bc7708ab.PNG
  • $$2.5ms^{-1}$$
  • $$1.25ms^{-1}$$
  • $$1.75ms^{-1}$$
  • $$2.75ms^{-1}$$
A piece of paper is in the form of square . Two corners of these square are folded to make it appear like figure $$2$$ . Both the corners are put together at center of square $$O$$ . If $$O$$ is taken to be $$(0,0)$$ , the center of mass of new will be :

1462282_4ee2ff1ac6bf41b791e687f509126350.png
  • $$\left( - \frac { a } { 8 } , 0 \right)$$
  • $$\left( - \frac { a } { 6 } , 0 \right)$$
  • $$\left( - \frac { a } { 12 } , 0 \right)$$
  • $$\left( \frac { a } { 12 } , 0 \right)$$
Two particles of masses m1 and m2 separated by a distance d are at rest initially. If they move towards each other under mutual interaction, where will they meet ?
  • at the centre of line joining the two particles
  • anywhere in between two masses
  • at the centre of mass of the system of two particles
  • none of the above
Distance of the center of mass of a solid uniform cone from its verted is zo. If the radius of its base isand its height is h, then zo is equal to 
  • $$\frac { h ^ { 2 } } { 4 R }$$
  • $$\frac { 3 h } { 4 }$$
  • $$\frac { 5 h } { 8 }$$
  • $$\frac { 3 h ^ { 2 } } { 8 R }$$
Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is $$r$$ . Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become


1449274_b6b878ea041641a29c4a0dbf96fd1db1.png
  • $$\left( \frac { r } { \sqrt [ 3 ] { 2 } } \right)$$
  • $$\left( \frac { 2 r } { \sqrt { 3 } } \right)$$
  • $$\left( \frac { 2 r } { 3 } \right)$$
  • $$\left( \frac { 1 } { \sqrt { 2 } } \right) ^ { 2 }$$
A thin rod of length 4l mass 4 m is bent at the points as shown in the fig. What is the moment of inertia of the rod about the axis passing point O& perpendiular to the plane of the paper
1476751_95992d87fcc944e2b00496a8b111a42d.png
  • $$\dfrac { { m\ell }^{ 2 } }{ 3 } $$
  • $$\dfrac { 10{ m\ell }^{ 2 } }{ 3 } $$
  • $$\dfrac { { m\ell }^{ 2 } }{ 12 } $$
  • $$\dfrac { { m\ell }^{ 2 } }{ 24 } $$
A rod of mass M and length L is kept on horizontal plane as shown. A force F is applied as shown what should be x so that the hinge offers no reaction ?
1527787_318e4ee84e844d43a4ce67c47f71b090.PNG
  • Zero
  • $$\dfrac { 2L }{ 3 } $$
  • $$\dfrac { L }{ 3 } $$
  • L
The linear mass density, $$\lambda (x)$$, for a one-dimensional object of length $$2{ x }_{ 0 }$$ is plotted in the graph. The location of the center of mass for this object, from origin is $$r_0$$ then $$\frac { 9{ r }_{ 0 } }{ { x }_{ 0 } } $$ is _____
1546967_830aa5f147664fcc92009027286a663f.png
  • 11
  • 15
  • 18
  • 25
If $$I_2$$ is the moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre of mass and $$I_2$$ is the moment of inertia of the ring formed by the same rod about an axis tangent to the ring and perpendicular to the plane of the ring, then find the ratio $$I_1/I_2$$
  • $$\cfrac {\pi^2} 3$$
  • $$\cfrac {\pi^2} 6$$
  • $$\cfrac {\pi^2} 2$$
  • $$\cfrac {\pi^2} 5$$
$$F = a\bar i + 3\bar j + 6\bar k\,\,and\;\,\bar r = 2\bar i - 6\bar j - 12\bar k.$$ The of $$'a'$$ for which the angular momentum same,duration of day will be 
  • $$-1$$
  • $$0$$
  • $$1$$
  • $$6h$$

A uniform heavy disc is rotating at constant angular velocity $$\omega $$ about a vertical axis through its center and perpendicular to the plane of the disc. Let $$L$$ be its angular momentum. A lump of plastic is dropped (gently) vertically on the edge of the disc and sticks to it. Which of the following will be constant
  • $$\omega $$
  • $$\omega $$ and L both
  • $$L$$ only
  • Neither $$\omega $$ nor $$L$$
The radius of gyration of a homogeneous solid cylinder, of length $$L$$ and radius $$R$$, for rotation about an axis perpendicular to its length through its one end is
  • $$\cfrac{L}{\sqrt{3}}$$
  • $$\sqrt{\cfrac{3}{2}}R$$
  • $$\cfrac { 1 }{ 2\sqrt { 3 } } { \left( 3{ R }^{ 2 }+4{ L }^{ 2 } \right) }^{ \cfrac { 1 }{ 2 } }$$
  • $$\sqrt { \cfrac { { R }^{ 2 } }{ 4 } +\cfrac { { L }^{ 2 } }{ 12 } } $$
A uniformly straight rod is placed in vertical position on a smooth horizontal surface and released. As the rod is in motion, the center of mass moves
  • Horizontally
  • Vertically down
  • In a parabolic path
  • Does not move
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 $${ ms }^{ -1 }$$ and the 3 kg body has the velocity of 2 $${ ms }^{ -1 }$$. The velocity of the centre of mass of that instant is 
  • 5 $${ ms }^{ -1 }$$
  • 1 $${ ms }^{ -1 }$$
  • 0
  • None of these
A canon shell moving along a straight line bursts into two parts. Just after the burst one part moves with momentum $$20$$ N s making an angle $$30^o$$ with the original line of motion. The minimum momentum of the other part of shell just after the burst is?
  • $$0$$ N s
  • $$5$$ N s
  • $$10$$ N s
  • $$17.32$$ N s
Two blocks of masses $$5$$kg and $$2$$kg are placed on a frictionless surface and connected by a spring. An external kick gives a velocity of $$14$$ m/s to the heavier block in the direction of lighter one. The magnitudes of velocities of two blocks in the centre of mass frame after the kick are, respectively.
  • $$4$$ m/s, $$4$$ m/s
  • $$10$$ m/s, $$4$$ m/s
  • $$4$$ m/s, $$10$$ m/s
  • $$10$$ m/s, $$10$$ m/s
A $$2kg$$ body and a $$3kg$$ body are moving along the x-axis. At a particular instant the $$2kg$$ body has a velocity of $$3m/s$$ and the $$3kg$$ has the velocity of $$2m/s$$. The velocity of the centre of mass at that instant is:-
  • $$5m/s$$
  • $$1m/s$$
  • $$0$$
  • $$\dfrac {12}{5}m/s$$
For the adjoining diagram , the correct relation between $$I_{1},I_{2}$$ and $$I_{3}$$ is, (I- moment of inertia)
1605729_d0332d57e0e3436abcc97bbb0ba485c2.png
  • $$I_{1} > I_{2}$$
  • $$I_{2} > I_{1}$$
  • $$I_{3} > I_{1}$$
  • $$I_{3} > I_{2}$$
A thin rod of length $$4\ l$$ and mass 4 m is bent at the points as shown in fig. what is moment of inertia of the rod about the axis passing through point O and perpendicular to the plane of the paper. 
1735376_0e872438fb0645d3bde62dd9f6b3af3b.PNG
  • $$ \frac { Ml^2}{3} $$
  • $$ \frac {10 Ml^2}{3} $$
  • $$ \frac { Ml^2}{12} $$
  • $$ \frac { Ml^2}{24} $$
A solid cylinder is released from the top of an inclined plane of height $$h$$. What will be the speed of its centre of mass on reaching the bottom?
  • $$\sqrt{2 \,gh}$$
  • $$\sqrt{4 \,gh}$$
  • $$\left[\dfrac{4}{3}gh \right]^{1/2}$$
  • $$\left[\dfrac{2}{3}gh \right]^{1/2}$$
A thin circular plate of mass $$M$$ and radius $$R$$ has its density varying as $$\rho (r) = \rho_{0}r$$ with $$\rho_{0}$$ as constant and $$r$$ is the distance from its centre. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is $$I = aMR^{2}$$. The value of the coefficient $$a$$ is
  • $$\dfrac {3}{2}$$
  • $$\dfrac {1}{2}$$
  • $$\dfrac {3}{5}$$
  • $$\dfrac {8}{5}$$
Three particles of masses $$50 g, 100 g$$ and $$150 g$$ are placed at the vertices of an equilateral triangle of side $$1 m$$ (as shown in the figure). The (x, y) coordinates of the centre of mass will be : 

1615198_7fbcfc30cb76447cb6c699bbf93ace9b.png
  • $$\left(\dfrac{7}{12} m , \dfrac{\sqrt{3}}{8} m\right)$$
  • $$\left(\dfrac{\sqrt{3}}{4} m, \dfrac{5}{12} m \right)$$
  • $$\left(\dfrac{7}{12} m , \dfrac{\sqrt{3}}{4} m\right)$$
  • $$\left(\dfrac{\sqrt{3}}{8} m, \dfrac{7}{12} m \right)$$
The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass $$4kg$$. (The coordinates of the same are shown in figure) are:
1697234_82f67d3df9dd4af8aae099e75c4364ab.png
  • $$(0.75m, \, 0.75m)$$
  • $$(1.25m, \, 1.50m)$$
  • $$(1m, \, 1.75m)$$
  • $$(0.75m, \, 1.75m)$$
An inverted T-shaped object is placed on a smooth horizontal floor as shown in Fig.
A force F is applied on the system as shown in Fig. The value of x so that the system performs pure translational motion is?

1735651_5f9180d762334e4a95e643ec570e9877.PNG
  • $$\dfrac{L}{4}$$
  • $$\dfrac{3L}{4}$$
  • $$\dfrac{L}{2}$$
  • $$\dfrac{3L}{2}$$
The ratio $$x_1 /x_2$$ is :
  • $$2$$
  • $$\dfrac{1}{2}$$
  • $$\sqrt 2$$
  • $$\dfrac{1}{\sqrt 2}$$
What is the moment of inertia of a triangular plate $$ABC$$ of mass $$M$$ and side $$BC='a'$$ about an axis passing through $$A$$ and perpendicular to the plane of the plate?
1742173_edcb471e0cf64b97b75bfb5efd5d941f.png
  • $$\dfrac{Ma^2}{6}$$
  • $$\dfrac{3Ma^2}{4}$$
  • $$\dfrac{Ma^2}{24}$$
  • $$\dfrac{Ma^2}{12}$$
The ratio$$ \frac {M}{m} $$,
  • $$ \frac {M}{m} = 10 $$
  • $$ \frac {M}{m} = 4 $$
  • $$ \frac {M}{m} = 8 $$
  • $$ \frac {M}{m} = 5 $$
In a certain unit, the radius of gyration of a uniform disc about its central and a uniform disc about its central and transverse axis is $$ \sqrt{2.5} $$. Its radius of gyration about a tangent in its plane (in same unit) must be 
  • $$ \sqrt{5} $$
  • $$ 2.5$$
  • $$ 2 \sqrt{2.5} $$
  • $$ \sqrt{12.5} $$
0:0:1


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