Physics - Rigid Body Dynamics

CODE

0

TEST - 10 TARGET : JEE (IITs) 2014 Date : 07-03-2013

COURSE CODE : CLINIC CLASSES VIKAAS(JA) & VIPUL(JB) Duration : 1 Hour

Max. Marks : 80

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

Physics - Rigid Body Dynamics

INSTRUCTIONS 2.

No additional sheets will be provided for rough work.

3.

Blank paper, clipboard, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed.

4.

The answer sheet, a machine-gradable Objective Response Sheet (ORS), is provided separately.

5.

Do not Tamper / mutilate the ORS or this booklet.

6.

Do not break the seals of the question-paper booklet before instructed to do so by the invigilators.

7.

Write your Name, Roll No. and Sign in the space provide on the back page of this booklet.

B. Filling the bottom-half of the ORS : Use only Black ball point pen only for filling the ORS. Do not use Gel / Ink / Felt pen as it might smudge the ORS. 8.

Write your Roll no. in the boxes given at the top left corner of your ORS with black ball point pen. Also, darken the corresponding bubbles with Black ball point pen only. Also fill your roll no on the back side of your ORS in the space provided (if the ORS is both side printed).

9.

Fill your Paper Code as mentioned on the Test Paper and darken the corresponding bubble with Black ball point pen.

10. If student does not fill his/her roll no. and paper code correctly and properly, then his/her marks will not be displayed and 5 marks will be deducted (paper wise) from the total. 11. Since it is not possible to erase and correct pen filled bubble, you are advised to be extremely careful while darken the bubble corresponding to your answer. 12. Neither try to erase / rub / scratch the option nor make the Cross (X) mark on the option once filled. Do not scribble, smudge, cut, tear, or wrinkle the ORS. Do not put any stray marks or whitener anywhere on the ORS. 13. If there is any discrepancy between the written data and the bubbled data in your ORS, the bubbled data will be taken as final. C. Question paper format and Marking scheme : 14. The question paper consists of 1 parts. The part consists of Two Sections. 15. For each question in Section–I, you will be awarded 3 marks if you darken the bubble(s) corresponding to the correct choice for the answer and zero mark if no bubbled is darkened. In case of bubbling of incorrect answer, minus one (–1) mark will be awarded. 16. For each question in Section–II, you will be awarded 5 marks if you darken the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In case of bubbling of incorrect answer, minus one (–1) mark will be awarded.

DO NOT BREAK THE SEALS WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR

A. General : 1. This Question Paper contains 22 questions.

PHYSICS

PART I : PHYSICS SECTION - I Straight Objective Type This section contains 15 multiple choice questions. Each question has choices (A), (B), (C), and (D) out of which ONLY ONE is correct. 1.

A ring of mass m and radius R rolls on a horizontal rough surface without slipping due to an applied force ‘F’. The friction force acting on ring is : (A)

F 3

(B)

2F 3

(C)

F 4

(D) Zero

2.

Two like parallel forces P and 3 P are 40 cm apart. If the direction of P is reversed, then the point of application of their resultant shifts through a distance of : (A) 30 cm (B) 40 cm (C) 50 cm (D) 60 cm

3.

As shown in figure, S is a point on a uniform disc rolling with uniform angular velocity on a fixed rough horizontal surface. The only forces acting on the disc are its weight and contact forces exerted by horizontal surface. Which graph best represents the magnitude of the acceleration of point S as a function of time

s

(A)

Space for Rough Work

(B)

(C)

(D)

Space for Rough Work

RESONANCE

JA&JBTEST10070313C0-2

PHYSICS

4.

A horizontal force F is applied at the top of an equilateral triangular block having mass m. The minimum coefficient of friction required to topple the block before translation will be

2 (A)

5.

3

(B)

1

1 2

(C)

3

(D)

1 3

Consider a uniform disc of mass ‘m’ performing pure rolling with velocity ‘v’ on a fixed rough surface : (A) Kinetic energy of upper half will be

3 mv2 8

(B) Kinetic energy of upper half will be less than

3 mv2 8

(C) Kinetic energy of upper half will be more than

3 mv2 8

(D) Kinetic energy of upper half will be more than

3 mv2 4

Space for Rough Work

RESONANCE

JA&JBTEST10070313C0-3

PHYSICS

6.

A disc of mass M and radius R has a spring of constant k attached to its centre, the other end of the spring being fixed to a vertical wall. If the disk rolls without slipping on a level floor, how far to the right does the centre of mass move, if initially the spring was unstretched and the angular speed of the disc was o .

(A) Ro2m/3k) 7.

(C) Rom/k)

(D) None of these

A small solid sphere of mass m is released from a point A at a height h above the bottom of a rough track as shown in the figure. If the sphere rolls down the track without slipping, its rotational kinetic energy when it comes to the bottom of track is

(A) mgh 8.

(B) Ro3m/2k)

(B)

10 mgh 7

(C)

5 mgh 7

(D)

2 mgh 7

In the figure shown a thin light inextensible string is wrapped around a uniform disc. One end of the string is fixed to the ceiling of the lift. Acceleration ‘a’ of the lift is such

a that the centre of disc does not move with respect to ground. Find the value of g . String does not slip on pulley. (A) 1

(B) 2

(C) 3

(D) 4

Space for Rough Work

RESONANCE

JA&JBTEST10070313C0-4

a

PHYSICS

9.

A uniform disc of radius R lies in the x-y plane, with its centre at origin. its moment of inertia about z-axis is equal to its moment of inertia about line y = x + c. The value of c will be (A) 

10.

R 2

R (B) ±

(C)

2

R 4

(D) –R

A uniform circular disc placed on a horizontal rough surface has initially a velocity v0 and an angular velocity 0 as shown in the figure. The disc comes to rest after moving some distance in the direction of motion. Then v0/0 is: v0 0

(A) R/2 11.

(C) 3 R/2

(D) 2

The moment of inertia of a hollow cubical box of mass M and side a about an axis passing through the centres of two opposite faces is equal to (A)

12.

(B) R

R

5 Ma2 3

(B)

5 Ma2 6

(C)

5 Ma2 12

(D)

5 Ma2 18

Two men of equal masses stand at opposite ends of the diameter of a turntable disc of a certain mass, moving with constant angular velocity. The two men make their way to the middle of the turntable at equal rates. In doing so (A) kinetic energy of rotation has increased while angular momentum remains same. (B) kinetic energy of rotation has decreased while angular momentum remains same. (C) kinetic energy of rotation has decreased but angular momentum has increased. (D) both, kinetic energy of rotation and angular momentum have decreased.

Space for Rough Work

RESONANCE

JA&JBTEST10070313C0-5

PHYSICS

13.

A ball of mass m moving with constant velocity u collides with a smooth horizontal surface at O as shown. Neglect gravity and friction. The y-axis is drawn normal to the horizontal surface at the point of impact O and x-axis is horizontal as shown. About which point will the angular momentum of ball be conserved.

(A) point A 14.

(B) point B

(C) point C

(D) None of these

A sphere rolls without sliding on a rough inclined plane (only mg and constant forces are acting on the body). The angular momentum of the body: (A) about centre is conserved (B) is conserved about the point of contact (C) is conserved about a point whose distance from the inclined plane is greater than the radius of the sphere (D) is not conserved about any point.

15.

In the figure shown a ring A is rolling without sliding with a velocity v on the horizontal surface of the body B (of same mass as A). All surfaces are smooth. B has no initial velocity. What will be the maximum height (from initial position) reached by A on B.

3 v2 (A) 4g

v2 (B) 4g

v2 (C) 2g

v2 (D) 3g

Space for Rough Work

RESONANCE

JA&JBTEST10070313C0-6

PHYSICS

SECTION - II Multiple Correct Answers Type This section contains 7 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE is/are correct. 16.

When a cylinder is spinned and placed somewhere on surface of a rough inclined plane as shown then after release.

(A) The cylinder may continue to accelerate down and never be in pure rolling. (B) The cylinder may accelerate up for some time then retard and come down in pure rolling. (C) The cylinder may accelerate down continuously and pure rolling will start after some time. (D) Friction will act on cylinder in upward direction initially and later it will be downward direction. 17.

A heavy homogenous cylinder has a mass m and radius R. It is accelerated by a horizontal force F, which is applied through a rope wound around a light drum of radius r attached to the cylinder. The coefficient of static friction is sufficient for the cylinder to roll without slipping : Choose the correct options : 2F (A) acceleration of centre of cylinder is a = (R + r) 3mR 21 r  (B) friction assumed to be in the opposite direction of F is f =    F 32 R r  R 

Space for Rough   (C) If Work

F 1 a will be greater than m 2

(D) Friction assumed to be in the direction of F is f =

21 r    F 32 R

Space for Rough Work

RESONANCE

JA&JBTEST10070313C0-7

PHYSICS

18.

A simple pendulum A and a homogeneous rod B hinged at its end are released from horizontal position as shown in figure. (A)

(B)

L

(A) The times period of swing of simple pendulum is greater than that of rod if L =  (B) The time period of swing of simple pendulm is equal to that of rod if L =  (C) The time period of swing of simple pendulum is greater than that of rod if L =

(D) The time period of swing of simple pendulum is equal to that of rod if L =

2 3

2 . 3

19.

A rigid body is in pure rotation, that is, undergoing fixed axis rotation. Then which of the following statement(s) are true. (A) You can find two points in the body in a plane perpendicular to the axis of rotation having same velocity. (B) You can find two points in the body in a plane perpendicular to the axis of rotation having same acceleration. (C) Speed of all the particles lying on the curved surface of a cylinder whose axis coincides with the axis of rotation is same. (D) Angular speed of the body is same as seen from any point in the body.

20.

Which of the following statements is/are true (A) work done by kinetic friction on an object may be positive. (B) A rigid body rolls up an inclined plane without sliding. The friction force on it will be up the incline. (only contact force and gravitational force is acting) (C) A rigid body rolls down an inclined plane without sliding. The friction force on it will be up the incline. (only contact force and gravitational force is acting) (D) A rigid body is left from rest and having no angular velocity from the top of a rough inclined plane. It moves down the plane with slipping. The friction force on it will be up the incline.

Space for Rough Work

RESONANCE

JA&JBTEST10070313C0-8

PHYSICS

21.

A particle is projected at an angle of projection (  900) with the horizontal. Let Vx, Vy be it’s horizontal and vertical components of its instantaneous velocity; x and y be it’s horizontal and vertical instantaneous displacements with respect to the point of projection. then as time increases: (A) yVx - xVy increases (B) The angular acceleration of the particle about the point of projection increases. (C) The angular velocity of the particle about the point of projection increases. (D) The path of the particle as seen by another projectile will be a straight line as long as they are in air.

22.

A uniform disc (with block) is rotating with constant angular speed  about vertical axis passing through its centre as shown in diagram. A small block of mass 'm' does not slip on disc and this block is also performing uniform circular motion with angular speed . Which of the following statements is/are correct :

(A) Power delivered by disc to the block is zero (B) Acceleration vector of block is not constant with time (C) Torque of normal force on block about vertical axis is zero (D) Torque of friction force on the block about vertical axis is zero

Space for Rough Work

RESONANCE

JA&JBTEST10070313C0-9