Rotation The Basic Definition(12th Grade > Physics ) Questions and answers for exam Preparation

12th Grade > Physics

ROTATION THE BASIC DEFINITION MCQs

Total Questions : 30 | Page 3 of 3 pages

Question 21. Four masses are joined to a light circular frame as shown in the figure. The radius of gyration of this system about an axis passing through the centre of the circular frame and perpendicular to its plane would be

a√2
a2
a
2a

Discuss Question

Answer: Option C. -> a
:
C
Since the circular frame is massless so we will consider moment of inertia of four masses only.

I = m a^{2} + 2 m a^{2} + 3 m a^{2} + 2 m a^{2} = 8 m a^{2}

.....(i)
Now from the definition of radius of gyration

I = 8 m k^{2}

.....(ii)
comparing (i) and (ii) radius of gyration k = a.

Question 22. Three point masses each of mass m are placed at the corners of an equilateral triangle of side a. The moment of inertia of system about the side AB is

ma2
3ma2
34ma2
23ma2

Discuss Question

Answer: Option C. -> 34ma2
:
C
The moment of inertia of system about AB side of triangle

I = I_{A} + I_{B} + I_{C}

= 0 + 0 + m x^{2}

= m {(\frac{a \sqrt{3}}{2})}^{2} = \frac{3}{4} m a^{2}

Three Point Masses Each Of Mass M are Placed At The Corners...

Question 23. The moment of inertia of HCl molecule about an axis passing through its centre of mass and perpendicular to the line joining the

H^{+}

and

C l^{-}

ions will be, if the interatomic distance is 1

o A

0.61×10−47kg.m2
1.61×10−47kg.m2
0.061×10−47kg.m2
0

Discuss Question

Answer: Option B. -> 1.61×10−47kg.m2
:
B
If

r_{1}

and

r_{2}

are the respective distances of particles

m_{1}

and

m_{2}

from the centre of mass then

m_{1} r_{1} = m_{2} r_{2} \Rightarrow 1 \times x = 35.5 \times (L - x) \Rightarrow x = 35.5 (1 - x)

\Rightarrow x = 0.973 o A

and

L - x = 0.027 o A

Moment of inertia of the system about centre of mass

I = m_{x}^{2} + m_{2} (L - x)^{2}

I = 1 a m u \times (0.973 o A)^{2} + 35.5 a m u \times (0.027 o A)^{2}

Substituting 1 a.m.u.

= 1.67 \times 10^{- 27} k g

and

1 o A = 10^{- 10} m

I = 1.62 \times 10^{- 47} k g m^{2}

The Moment Of Inertia Of HCl Molecule About An Axis Passing ...

Question 24. Three rods each of length L and mass M are placed along X, Y and Z-axes in such a way that one end of each of the rod is at the origin. The moment of inertia of this system about Z axis is

2ML23
4ML23
5ML23
7ML23

Discuss Question

Answer: Option A. -> 2ML23
:
A
Moment of inertia of the system about z-axis can be find out by calculating the moment of inertia of individual rod about z-axis

I_{1} = I_{2} = \frac{M L^{2}}{3}

because z-axis is the edge of rod 1 and 2
and

I_{3} = 0

because rod in lying on z-axis

∴ I_{S y s t e m} = I_{1} + I_{2} + I_{3} = \frac{M L^{2}}{3} + \frac{M L^{2}}{0} + 0 = \frac{2 M L^{2}}{3} .

Three Rods Each Of Length L And Mass M Are Placed Along X, Y...

Question 25. Two identical rods each of mass 'M' and length 'l' are joined in crossed position as shown in figure. The moment of inertia of this system about a bisector would be

Ml26
Ml212
Ml23
Ml24

Discuss Question

Answer: Option B. -> Ml212
:
B
Moment of inertia of system about an axes which is perpendicular to plane of rods and passing through the common centre of rods

I_{z} = \frac{M l^{2}}{12} + \frac{M l^{2}}{12} = \frac{M l^{2}}{6}

Again from perpendicular axes theorem

I_{2} = I_{B_{1}} + I_{B_{2}} = 2 I_{B_{1}} = 2 I_{B_{2}} = \frac{M l^{2}}{6}

[As

I_{B_{1}} = I_{B_{2}}]

∴ I_{B_{1}} = I_{B_{2}} = \frac{M l^{2}}{12} .

Question 26. Four spheres, each of mass 'M' and radius 'r' are situated at the four corners of square of side 'R'. The moment of inertia of the system about an axis perpendicular to the plane of square and passing through its centre will be

52M(4r2+5R2)
25M(4r2+5R2)
25M(4r2+5r2)
52M(4r2+5r2)

Discuss Question

Answer: Option B. -> 25M(4r2+5R2)
:
B
M. I. of sphere A about its diameter

I_{O^{'}} = \frac{2}{5} M r^{2}

Now M.I. of sphere A about an axis perpendicular to the plane of square and passing through its centre will be

I_{O} = I_{O^{'}} + M {(\frac{R}{\sqrt{2}})}^{2} = \frac{2}{5} M r^{2} + \frac{M R^{2}}{2}

Moment of inertia of system (i.e. four sphere)

= 4 I_{O} = 4 [\frac{2}{5} M r^{2} + \frac{M R^{2}}{2}] = \frac{2}{5} M [4 r^{2} + 5 R^{2}]

Question 27. The moment of inertia of a rod of length 'l' about an axis passing through its centre of mass and perpendicular to rod is 'I'. The moment of inertia of hexagonal shape formed by six such rods, about an axis passing through its centre of mass and perpendicular to its plane will be

Discuss Question

Answer: Option C. -> 60l
:
C
Moment of inertia of rod AB about its centre and perpendicular to the length

= \frac{m l^{2}}{12} = l ∴ m l^{2} = 12 l

Now moment of inertia of the rod about the axis which is passing through O and perpendicular to the plane of hexagon

l_{r o d} = \frac{m l^{2}}{12} + m x^{2}

[From the theorem of parallel axes]

= \frac{m l^{2}}{12} + m {(\frac{\sqrt{3}}{2} l)}^{2} = \frac{5 m l^{2}}{6}

Now the moment of inertia of system

l_{s y s t e m} = 6 \times I_{r o d} = 6 \times \frac{5 m l^{2}}{6} = 5 m l^{2}

l_{s y s t e m} = 5 (12 l) = 60 l

[As

m l^{2} = 12 l]

The Moment Of Inertia Of A Rod Of Length 'l' About An Axis P...

Question 28. Angular displacement

θ

of a flywheel varies with time as

θ = a t + b t^{2} + c t^{3}

, then angular acceleration of the flywheel is given by

a+2bt−3ct2
2b−6t
a+2b−6t
2b+6ct

Discuss Question

Answer: Option D. -> 2b+6ct
:
D
Angular acceleration

α = \frac{d^{2} θ}{d t^{2}} = \frac{d^{2}}{d t^{2}} (a t + b t^{2} + c t^{3}) = 2 b + 6 c t

Question 29. Let 'l' be the moment of inertia of an uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle

θ

with AB. The moment of inertia of the plate about the axis CD is then equal to

I
Isin2θ
Icos2θ
Icos2θ2

Discuss Question

Answer: Option A. -> I
:
A
Let

I_{z}

is the moment of inertia of square plate about the axis which is passing through the centreand perpendicular to the plane.

I_{Z} = I_{A B} + I_{A^{'} B^{'}} = I_{C D} + I_{C^{'} D^{'}}

[By the theorem of perpendicular axis]

I_{Z} = 2 I_{A B} = 2 I_{A^{'} B^{'}} = 2 I_{C D} = 2 I_{C^{'} D^{'}}

[As AB, A' B' and CD, C' D' are symmetric axis]
Hence

I_{C D} = I_{A B} = I

Let 'l' Be The moment Of Inertia Of An Uniform Square Plate...

Question 30. The wheel of a car is rotating at the rate of 1200 revolutions per minute. On pressing the accelerator for 10 seconds, it starts rotating at 4500 revolutions per minute. The angular acceleration of the wheel is