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 1 of 3 pages

Question 1. Four thin rods of same mass 'M' and same length 'l', form a square as shown in the figure. Moment of inertia of this system about an axis through centre O and perpendicular to its plane is

43Ml2.
Ml23
Ml26
23Ml2.

Discuss Question

Answer: Option A. -> 43Ml2.
:
A
Moment of inertia of rod AB about point

P = \frac{1}{12} M l^{2}

M.I. of rod AB about point

O = \frac{M l^{2}}{12} + M {(\frac{1}{2})}^{2} = \frac{1}{3} M l^{2}

[by the theorem of parallel axis]
and the system consists of 4 rods of similar type so by the symmetry

I_{S y s t e m} = \frac{4}{3} M l^{2} .

Question 2. Let 'I' be the moment of inertia of a 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
Icos2(θ2)

Discuss Question

Answer: Option A. -> I
:
A

I_{A B} = I_{A^{'} B^{'}} = I a n d I_{C D} = I_{C^{'} D^{'}}

I_{0}

be the moment of inertia of the square plate about an axis passing through O and perpendicular to the plate, then by the perpendicular axis theorem

I_{0} = I_{A B} + I_{A^{'} B^{'}} = 2 I_{A B} . . . . (1)

I_{0} = I_{C D} = I_{C^{'} D^{'}} = 2 I_{C D} . . . . (2)

From ((1) and (2))

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

Let 'I' Be The Moment Of Inertia Of A Uniform Square Plate A...

Question 3. If the position vector of a particle is

⃗ r = (3 ˆ i + 4 ˆ j)

meter and its angular velocity is

⃗ ω = (ˆ j + 2 ˆ k)

rad/sec then its linear velocity is (in m/s)

(8ˆi−6ˆj+3ˆk)
(3ˆi+6ˆj+8ˆk)
-(3ˆi+6ˆj+6ˆk)
(6ˆi+8ˆj+3ˆk)

Discuss Question

Answer: Option A. -> (8ˆi−6ˆj+3ˆk)
:
A

⃗ v = ⃗ ω \times ⃗ r = (3 ˆ i + 4 ˆ j + 0 ˆ k) \times (0 ˆ i + ˆ j + 2 ˆ k) = ∣ ∣∣∣ ∣ \begin{matrix} ˆ i & ˆ j & ˆ k 3 & 4 & 0 0 & 1 & 2 \end{matrix} ∣ ∣∣∣ ∣ = 8 ˆ i - 6 ˆ j + 3 ˆ k

Question 4. A wheel is at rest. Its angular velocity increases uniformly and becomes 60 rad/sec after 5 sec. The total angular displacement is

600 rad
75 rad
300 rad
150 rad

Discuss Question

Answer: Option D. -> 150 rad
:
D
Angular acceleration

α = \frac{ω_{2} - ω_{1}}{t} = \frac{60 - 0}{5} = 12 r a d / s e c^{2}

Now from

θ = ω_{1} t + \frac{1}{2} α t^{2} = 0 + \frac{1}{2} (12) (5)^{2} = 150 r a d .

Question 5. The moment of inertia of a solid sphere of density

ρ

and radius R about its diameter is

105176R5ρ
105176R2ρ
176105R5ρ
176105R2ρ

Discuss Question

Answer: Option C. -> 176105R5ρ
:
C
Moment of inertia of sphere about it diameter

I = \frac{2}{5} M R^{2} = \frac{2}{5} (\frac{4}{3} π R^{3} ρ) R^{2}

[A s M = V ρ = \frac{4}{3} π R^{3} ρ]

l = \frac{8 π}{15} R^{5} ρ = \frac{8 \times 22}{15 \times 7} R^{5} ρ = \frac{176}{105} R^{5} ρ

Question 6. As a part of a maintenance inspection the compressor of a jet engine is made to spin according to the graph as shown. The number of revolutions made by the compressor during the test is

9000
16570
12750
11250

Discuss Question

Answer: Option D. -> 11250
:
D
Number of revolution = Area between the graph and time axis = Area of trapezium

= \frac{1}{2} \times (2.5 + 5) \times 3000 = 11250

revolution.

Question 7. A circular disc X of radius 'R' is made from an iron plate of thickness 't', and another disc Y of radius '4R' is made from an iron plate of thickness '

\frac{t}{4}

'. Then the relation between the moment of inertia

I_{x}

and

I_{y}

Iy=64Ix
Iy=32Ix
Iy=16Ix
Iy=Ix

Discuss Question

Answer: Option A. -> Iy=64Ix
:
A
Moment of Inertia of disc

I = \frac{1}{2} M R^{2} = \frac{1}{2} (π R^{2} t ρ) R^{2} = \frac{1}{2} π t ρ R^{4}

[As

M = V \times ρ = π R^{2} t ρ

where t = thickness,

ρ

= density]

∴ \frac{I_{y}}{I_{x}} = \frac{t_{y}}{t_{x}} {(\frac{R_{y}}{R_{x}})}^{4}

[ If

ρ

= constant]

\Rightarrow \frac{I_{y}}{I_{x}} = \frac{1}{4} (4)^{4} = 64

[G i v e n R_{y} = 4 R_{x}, t_{y} = \frac{t_{x}}{4}]

\Rightarrow I_{y} = 64 I_{x}

Question 8. Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

Discuss Question

Answer: Option B. -> 6 l
:
B
Moment of inertia of disc about a diameter