Pg Brainstormer - 9c (Mechanics)635526719868222666

PG Brainstormer - 9C

PG Brainsto Brainstormer rmer - 9 C RIGID BODY DYNAMICS & CONSERV CONSERVATION ATION LAWS

An Ultimate Tool to understand advanced High School Physics

Ti m e A l l ow ed

by ASHISH ARORASir

4 5 M in

M ax i m um M ark s

45

Instruction : In Section - A each question from from 1 to 15 is of 3 Marks and and there is a negative marking of -1 Mark.

Section - A Single Choice Correct Type Questions (Q. No. 1 to 15)

Y X A L A G S C I S Y H P

In this section 15 questions are there and each question has four choices (A), (B), (C) and (D) out of which which ONLY ONE is correct. Marking Markin g Scheme - +3 for RIGHT answer and -1 for WRONG answe answer. r. 1.

A massless string strin g is wrapped wrapped around ar ound a hollow cylinder cylinder having ha ving mass m and radius r . The cylinder is kept on a rough horizontal hori zontal surface sur face (coefficient of friction is µ). A constant constan t force F is is applied as shown in the figure. In case of pure rolling, th e friction force acting on the bottom most point of the cylinder is : (B) µmg (A) 0 (C)

2.

mg 2

(D)

F

C

3mg

A

2

A uniform rod of mass ‘ m’ and length ‘ L’ is rigidly fixed to an axis, making maki ng an angle a ngle ‘ ’ with with it as as

axis

shown in the figure. The rod is r otated about this axis so that the free end of the rod moves m oves with with a uniform speed ‘ v’. the angular momentum of the rod about the axis is : (A)

1 3

mvL sin 

(B)

(C) mvL cos  3.

4.

1

3

A

(D) None of the above

A sphere is moving towards +ve x-axis with a velocity vc and rotates clockwise with angular speed  as shown in the figure, such that vc >  R. The instantaneous in stantaneous axis of rotation will be : (A) on point P

(B) on point P'

(C) insi nside the sphere here

(D) ou outside ide the the sphere here..

P’

 vc C

P

Consider the shown mechanism ABC . At a certain instan t block C was was found to be moving with a speed of 1 m/s

(B)

(C) 3 /4 m/s

(D) 2 3 m/s

B

L

3 /2 m/s

(A) 1/2 m/s

L C

30

A

Consider a body, body, shown in figure, consisting of two identical balls, each

of mass M connected connected by a light rigid rod. If an impulse J = = MV is is imparted M to the body at one of its ends, what would be its angular velocity? velocity? (A) V/L (B) 2V/L (C) V/3L 6.



mvL sin 

to the right. At th is instant what is the mag nitude of vertical component of velocity velocity of B :

5.

B

the maximum in clination of the plane of base of of rim from the horizontal is : –1 –1 (A)  = sin (sin ) (B)  = sin (2 sin ) (C)  P HYS ICS

M J = = MV

(D) V/4L

A hemispherical shell rests on a rough inclined plane whose angle of friction is

= sin –1 (3 sin

L

)

(D) 

= sin –1 (4 sin

, then



) 1

PG Brainstormer - 9C 7.

A uniform disc of radius 2 3 m is moving on a horizontal surface whose coefficient of friction is sufficient to prevent slipping at any instant of time. At some instant its angular velocity is 1 rad/sec and angular acceleration is 3 rad/s2. If at this instant, a point P on the disc has no acceleration, then the position vector of point P with respect to a frame moving with lin ear velocity, same as the velocity of centre of mass of the disc and origin lies on the centre of the disc at all instant as shown in t he figure :

8.

(A) 1.5 (iˆ  3 ˆj )

(B) 1.5 (iˆ  3 ˆj )

(C) 2.5 (iˆ  3 ˆj )

(D) 2.5 (iˆ  3 ˆj )

 

r

x

O P


A rectangular metal plate ABCD is supported by two hinges P1 and P2 so that it remains in equilibrium in vertical plane (with line AB vertical) as shown in the figure. Th e reaction forces R1 and R2 exerted by hinges on the metal plate is best, depicted by :

R1

(A)

R1

P1

A

D

R1

P1

(B)

R2

C

P2 B

D

A

P2 B

C

A

D

P1

R1

P1

(C)

R2

P2

B

9.

D

A

(D)

R2

R2

C

P2

B

C

A wheel rotates about an axle due to the friction of axle it experiences a retardation which is proportional to its angular velocity . It completes n revolutions when angular velocity falls to half of the initial value. How many more revolutions will it make before coming to rest? (A) 2n

(B) n

(C) n/2

(D) n/3

Paragraph for Question Nos. 10 to 12

A cylinder of mass m and radius R is rolling without slipping on a horizontal surface with angular velocity 0. The velocity of centre of mass of cylinder is 0 R. The cylinder comes across a step of height R/4. (Assume required friction is present at edge of the step so that cylinder does not slip at the edge) Answer the following questions based on above information.

O

0 R

10.

R/4

(C) 20/3

(D) 60/5

Find the minimum angular velocity ( 0) of cylinder so that cylinder rides up the step without slipping or jumping : (A)

12.

R

Then the angular velocity of cylinder just after the collision is (Assume cylinder remains in contact an d no slipping occurs on the edge of the step) : (A) 50/6 (B) 0

11.

0 R

2

3g

5

R

(B)

3 3g 5 R

(C)

5

3g

2

R

(D)

g

3 R

Find the maximum angular velocity ( 0) of cylinder so that cylinder rides up the step without jumping : (A)

PHYSICS

3 3g 5 R

(B)

2

3g

5

R

(C)

1

3g

2

R

(D)

1

g

2

3 R

2

PG Brainstormer - 9C Paragraph for Question Nos. 13 to 15 Crank shaft mechanism is a classic example of converting rotational motion into translation motion. The flywheel is performing rotation motion while the piston is performing pure translation motion. The engine rotates the flywheel at a constant angular velocity . A rod AB of length l, hinged at points A and B connects the flywheel with the piston. (Assume l >> r ).

A l

r O

Y X A L A G S C I S Y H P Piston



13.

The magnitude of velocity of piston as a function of time (at t = 0 points O,A and B were in a line.) (A) ( l + r cos t )

14.

15.

 r  (C) r   1  cos t  sin t (D) None of these  l 

(B) r  sint

The motion of point A on th e flywheel is : (A) periodic (B) oscillatory

(C) simple harmonic

(D) None of these

Magnitude of angular velocity of the rod as a function of time is : (A)

 r   l  sin t  

(B)

 r   l  cost  

*

PHYSICS

(C)

*

*

*

 r   l   

(D) None of these.

*

3


PG Brainstormer - 9 C RIGID BODY DYNAMICS & CONSERVATION LAWS


Time Allow ed

by ASHISH ARORASir

M aximum M arks

45 M in 45


OMR Sheet for the PG Brainstormer - 9 C (MECHANICS) A

B

C

D

A

1

11

2

12

3

13

4

14

5

15

B

C

D

6 7 8 9

10

PHYSICS

4


PG Brainstormer - 9 C RIGID BODY DYNAMICS & CONSERVATION LAWS


Time Allow ed

by ASHISH ARORASir

45 M in

M aximum M arks

45

A N S W ER K E Y

Section - A 1. (A) 10. (A)

PHYSICS


2. (A) 11. (A)

3. (D) 12. (A)

4. (B) 13. (C)

5. (A) 14. (A)

6. (B) 15. (B)

7.

(A)

8.

(C)

9.

(B)

5

Pg Brainstormer - 9c (Mechanics)635526719868222666

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