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Rotational Mechanics

Solution for Class 11, Physics, Rotational Mechanics

Question 1

ratio of their acceleration will be

$15 : 14$
$14 : 15$
$5 : 3$
$3 : 5$

Topic:

Rotational Mechanics

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Question 2

When a body rotates about an axis the quantity which remains same for all its particles, is

Linear velocity::Angular velocity
Angular momentum

Topic:

Rotational Mechanics

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Question 3

2. A

60 kg

load is hung from a steel wire. (a) Deters N-m (clockwise) \&

286 \cdot 6 N

-m (counter clockwise)] a horizontal force of

30 kg

wt. (b) If the wire is

1.3 m

long what horizontal force is repe if the load is held to one side with of

0.5 m

form the vertical line through the point of support. 3. Two ropes

X

and

Y

suspended from the ceilling of a room holds a

50 kg

body. Rope

X

makes an angle of 30 with the horizontal and the rope

Y

makes an angle of

6 0^{\circ}

with the horizontal. Find the tension in each rope. 4. An electric light fittings is supported in a room by means of wires respectively [Ans.

25 kg wt; 43 \cdot 3 kg

wt] attached to nails in the same horizontal plane in two opposite walls, the walls being

2.7432 m

apart. If the fiting weigh

4536 kg

, find the tension in each wire. 5. A light

rod A B

of length

3.6576 m

is hinged at

A

to a wall and carries a load

45.36 kg

at the other end

B

. Th? rod is kept horizontal by means of a rope one end of which is attached to the end

B

and the other end attached to a poin on wall

2.7432 m

vertically above the hinge. Find the tension in the rope and the push of the rod. Neglect the weigh of the rod. 6. A uniform steel bar

1524 m

long weighing

27.216 kg

is hinged at one end to a vertical wall and supported b a wire from the other end to a point on the wall

3.6576 m

vertically above the hinge. Find the tension in the wire an the reaction of the hinge. 7. Ans. 14

1442 kg wt; 14742 kg

wt directed

67 \cdot 3 8^{\circ}

with the horizonta 7. An adising sign weighing

9.072 kg

is suspended at the end of a horizontal bar weighing

2 \cdot 268 kg

and 1:828

m

long. The bar is hinged to a vertical wall at the other end and is kept horizontal by a wire fastened to its mid-poi and to a point on the wall

12192 m

above the hinge. Calculate the tension in the wire. [Ans,

25 \cdot 515 kg w

Topic:

Rotational Mechanics

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Question 4

NCERT Booster Program (NBTS) for NEET-2023 1. The position of centre of a mass of uniform Lshaped Lamina with dimensions as shown in figure below is

$\frac{5}{6}, \frac{5}{6}$
$\frac{5}{4}, \frac{5}{4}$
$\frac{5}{3}, \frac{5}{3}$
$\frac{5}{2}, \frac{5}{2}$

Topic:

Rotational Mechanics

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Question 5

108 System of Particles and Rotational Motion Previous Years Questions 51. An

L

-shaped object, made of thin rods of uniform (1)

\frac{20}{3}

mass density, is suspended with a string as shown in figure. If

A B = BC

, and the angle made by

A B

with downward vertical is

θ

, then (3)

\frac{30}{2}

[JEE (Main)-2019] 54. A homogeneous solid and mass

M

is pulle horizontal force. Assu angular acceleration (1)

tan θ = \frac{1}{2}

(2)

tan θ = \frac{2}{3}

(1)

\frac{F}{2 m R}

(3)

tan θ = \frac{1}{3}

(4)

tan θ = \frac{1}{2 3}

(3)

\frac{F}{3 m R}

Topic:

Rotational Mechanics

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Question 6

14. State and explain parallel and perpendicular axis theorem. (3 each) 16. Find the expression for the resultant of two forces using parallelogram law.

(5 m)

16. Define moment of inertia, radius of guration, angular momentum axis of rotation, axis o pretession, ceurtre of mass. 17. State and explain Pascal's law 18. Derive an expression for the pressure at a point in the liquid. 19. Define three moduli of elasticity. And explain stress strain graph. 20. Define three types of coefficient of expansions 21. Write the laws of thermal conduction and define its coefficient. 22. State zeroth, first and secund law of thermodynamics. 23. Explain Carnot's engine. 24. Derive an expression for displacement in cose of SHM. 25. Write the expressions for velocity, acceleration, KE, PE and TE in SHM.\& derive 26. Explain Newton's formula for velocity of sound. 27. Explain Laplace's correction for velc city of sound. 28. Write any four properties of stationary waves, sound waves, 29. derive the expressions for harmonics or frequencies in case of 1. closed pipe. 2. open pipe. 3.stretched string. 30) Benvoublis prinicple equ o continuity 31)

T =\to \times F

(detivation).

Topic:

Rotational Mechanics

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Question 7

Q) A Ciisc of Radius '

R

' is cut off from a clithon thin sheet of Mletal a cisrular Hole of Radius

\frac{R}{2}

is now ist out from the disc wim the role beng tangent to the ring. of the dis find the dist of beom foom the centse of origal disc

Topic:

Rotational Mechanics

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Question 8

एक स्थिर अक्ष के चारों ओर घूमने के लिए स्वतंत्र एक समान वेलन के चारों ओर एक रस्सी को लेेटा जाताहै जैसा कि दाई ओर दिखाया

^{2 m + M}

गया है। रस्सी को बेलन के भार के बराबर बल

F

से खींचा जाता है। रस्सी का त्वरण क्या है ? (A)

2 g

(B)

g

(C)

g /2

(D)

g /4

नगण्य दव्यमान की एक छड़ के सिरे से जुड़ा

10 kg

का द्रव्यमान

30 cm

त्रिज्या के एक वृत्त में

10 rad / s

. के कोणीय वेग से घूम रहा है। यदि इस द्रव्यमान को ब्रेक द्वारा

10 s

में विरामवस्था में लाया जाता है, तो लगाए गए बल आधूर्ण का परिमाण क्या है ? (A)

0.9 Nm

(B)

1.2 Nm

(C)

2.3 Nm

(D)

0.5 Nm

Topic:

Rotational Mechanics

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Question 9

ξ x \to

Spheoe,

m = 5 kg, R = 1 m, ω_{i} = 5 rmd pec

V_{i} = 10 m / s

find the Velocity of solid sphere When it Stats Pure Roline

Topic:

Rotational Mechanics

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Question 10

Naresh Sirui OPLE THO 048 04 86 OS 6.4 02 455-100/200 KHE Spring Constant T² (3²) 50 100 6 ERLE દર 2 16/u/22 Scale Xakis - lumit - 50x10³kg Yaxis - Iwnit 0.152' A 200 0 Name of Experime

Topic:

Rotational Mechanics

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Question 11

As per the given figure, a small ball P slides down the quadrant of a circle and hits the other ball

Q

of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball Q after collision will be

: (g = 10 m / s^{2})

0
$0.25 m / s$
$2 m / s$
$4 m / s$

Topic:

Rotational Mechanics

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Question 12

Molar specific heat of oxygen at constant pressure

C_{p} = 7.2 cal / mol /^{\circ} C

and

R = 8.3 J / moll_{k}

. constant volume, 5 mol of oxygen is heated from

1 0^{\circ} C

2 0^{\circ} C

, the quantity of heat requice approximately

$25 cal$
$50 cal$
$250 cal$
$500 cal$
By Mayer's formula $C_{v} = C_{p} - R = 7.2 - 2 \approx 5 caV / mol^{\circ} C$

Topic:

Rotational Mechanics

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Question 13

nalural numbon (2) ind MI abaul any side (2) - H- - - assing Horsiagonal - dicular toplane of se vare and 1 to plane of square.

Topic:

Rotational Mechanics

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Question 14

x

-axis. (b) State and prove perpendicular axis theorem. (c) Define M.A., V.R. and efficiency of a simple lifting machine and derive the relationship between them. (d) A body of weight of

50 N

is pulled along a rough horizontal plane by a force of

18 N

ANSWERS TO (a) What is resultant force? Ans. If a number of forces are acting taneously on a particle, then a single force which roduce the same effect as that of all the given forces wn as a resultant force. The resultant force of all mponents of forces can be found out analytically hically.

Topic:

Rotational Mechanics

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Question 15

A, B, C

का mass

m

है, और दूरी

L

है।

तो c_{m} = \frac{m _{1} r _{1} + m _{2} r _{2} + m _{3} r _{3} \dots\dots}{m _{1} + m _{2} + m _{3}}

Topic:

Rotational Mechanics

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Question 16

(4) By using formula calculate volume of a cylinder. Observations: (1) Smallest division on the main scale

= Y = \dots\dots\dots . cm

. (2) Total no. of divisions on the vernier scale

(N) =

div. (3) Least count

= \frac{Smallest division M.S.}{Number of divisions on V.S.}

= \frac{Y}{N}

(4)

Zero error = Z

cm

=

cm

(with proper sign)

Topic:

Rotational Mechanics

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Question 17

(c)

- 21 i^{\land} + 4 j^{n} + 4 k^{n}

(d)

- 14 i^{\land} + 38 j^{\land} - 16 k^{\land}

मूल बिंदु के परित: बल

F = - 3 i^{\land} + j^{\land} + 5 k^{\land}

का बल आघूर्ण ज्ञात कीजिए। यदि बल जिस कन पर लगता है उसकी स्थिति सदिश

r = 7 i^{\land} + 3 j^{\land} + i^{\land}

है। (a)

14 i^{\land} - 38 j^{\land} + 16 k^{\land}

(b)

4 i^{\land} + 4 j^{\land} + 6 k^{\land}

(c)

- 21 i^{\land} + 4 j^{\land} + 4 k^{\land}

(d)

- 14 i^{\land} + 38 j^{\land} - 16 k^{\land}

Topic:

Rotational Mechanics

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Question 18

Q) Particle strikes the

rod 4

sticks to it then just afterthe cowsion, find

w

of rod. a)

ω = \frac{6 V _{0}}{l}

ω = \frac{6 V _{0}}{5 l}

ω = \frac{6 V _{0}}{7 l}

Topic:

Rotational Mechanics

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Question 19

Atc., disc is in contact with ground and at

c_{2}

with string. At the other end string is connected So, there should not be any slip at

c_{1}

between disc and ground and at

c_{2}

between disc and sttirg: Following two examples illustrate the method of making these equations. Example 20 Consider the arrangement shown in figure. The string is wrapped around a uniform cylinder which rolls without slipping. The other end of the string is passed over a massless, frictionless pulley to a falling weight. Determine the acceleration of the falling mass

m

in terms of only the mass of the cylinder

M

, the mass

m

and g. Solution Let

T

be the tension in the string and

f

the

Topic:

Rotational Mechanics

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Question 20

Q.12 A square sheet of edge length

L

and uniform mass per unit area

σ

is used to form a hollows moment of inertia of this cylinder about the central axis is

$\frac{2 σ L ^{4}}{π ^{2}}$
$\frac{σ L ^{4}}{4 π ^{2}}$
$σ L^{2}$
$\frac{σ L ^{4}}{3 2 π ^{2}}$

Topic:

Rotational Mechanics

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Solution for Class 11, Physics, Rotational Mechanics

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