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PG Brainstormer - 8C
PG Brainsto Brainstormer rmer - 8 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
6 0 M in
M ax i m um M ark s
60
Instruction : In Section - A each question from from 1 to 20 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 20)
Y X A L A G S C I S Y H P
In this section 20 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.
2.
A sphere of mass M and and radius R is moving on a r ough fixed surface, having coefficient efficient of friction µ as shown in figure. It will attain a minimum linear velocity after at time : (A) V 0 / µg (B) 0 R/µg /µg (C) (V 0 – 0 R)/ µg (D) 2 ( V 0 – 0 R)/7µg
0
V0
A thin uniform equilateral equilatera l triangular plate rests in a vertical plane with one of its ends (A) on on a rough horizontal floor and the other end (C) ( C) on a smooth vertical wall. The Th e least angle its base (AC) can make with horiz ontal will be:
(A) = cot –1 2
(C) = tan –1 2
3
(B) = tan –1 2
2 3
(D) = cot –1 2
1
1
3
1
B
2 3 1
C
A
3.
(A) 4.
40 N 7
(B)
20 N 7
(C) 20 N
As shown in the diagram a frame which is initially in the horizontal plane is rotated about ‘ AB’. Find the angular velocity of the system at the moment it comes in a vertical plane from the initial position. (Assume it being made up of uniform rods of length l & l/2 (mass of length l = m) (A) = (C) =
5.
D
A solid solid sphere mass 10 kg and a nd radius r adius 0.1 m is p laced on a rough horizontal h orizontal surface. A 20 N force is applied on the sphere horizontally passing th rough centre of mass. For pure rolling, r olling, the force of friction is :
3g
33l
48 g 17l
(B) =
(D) =
(D) None
A
B
86 g
H
J l/2
l/2
D m/2
C
33l
8g
F
m/2
7l
G
E
A solid sphere mass M 0 is initially rotating with angular velocity velocity 0. If the radius of the sphere spher e is suddenly reduced to half then find the work done by friction friction of the liquid medium in which its is kept after contraction to bring it to rest. (Radius of sphere = R) (neglect air drag) (A)
P HYS ICS
2 M R22 5 0
(B) M 0 R22
(C)
4 5
M 0 R22
(D)
1
M R202 2 0
1
6.
PG Brainstormer - 8C At some instant a particle on a body is moving along a straight line 2 x – 3 y = 2 and its co-ordinate on that line is (4, 2). Now at other instant same particle is moving along a straight line 3 x + 4 y = 7 and its co-ordinate is (1, 1). Find the co-ordinate of that axis about which it is pure rotation : (A)
7.
30 35 , 17 17
(B)
(B) 10 3
(C)
2 R
(B)
2
5 gd
7 R
d
2
O
C
(D)
5 d ( g R)
7
R
2
v
(B) R –
v
(C) R +
R
(D) R –
2
R
2
A stick of length l and mass m lies on a frictionless horizontal surface on which it is free to move in any direction. A ball of same mass m moving with speed v0 perpendicularly to this length and collide at the end of stick. Find the angular velocity of rod if the collision is perfectly inelastic :
(C)
12 v0 7l
(B)
24v0 5l
(D)
6v0 5l
3v0 7l
A hollow sphere of mass 2 kg is kept on a rough h orizontal surface. A force of 10 3 N is applied as shown in the figure. Find the minimum value of ‘µ’ so that the sphere starts pure rolling. (Take g = 10 m/s 2) (A) 0.3 (B) 0.2 (D) for no value of µ it will start pure rolling (C) 0.1 A uniform disc of radius r is rotated in clockwise sense with angular speed Which of the graph of vcm – t can be correct :
(A)
vcm
F =
(B)
vcm
(D)
t
t
A uniform circular disc of radius r is placed on a rough horizontal surface and given a linear velocity v0 and angular velocity 0 as shown. The disc comes to rest after moving some distance to the right. It follows that : (A) 3 v0 = 20r (B) 2v0 = 0r (C) v0 = 0r (D) 2v0 = 30r
PHYSICS
3 N
and kept vertically on a rough surface.
(C)
t
10
30º
v cm
vcm
t
13.
(D) None of these
ˆ ) . There is a particle A disc of radius R rolls on a horizontal surface with linear velocity viˆ and angular velocity (– k P on the circumference of the disc which has velocity in vertical direction. The height of that particle from the ground will be :
(A)
12.
(C) 20
2
5 d ( g R) 2 2 R
(A) R +
11.
(D) None of these
Y X A L A G S C I S Y H P
5 gd
2
10.
8 16 , 9 9
A solid sphere of mass m and radius R is rolling on a rough surface, whose centre of mass is at C at a distance d from centre of sphere and at a certain instant it has angular velocity . Find the angular acceleration of sphere at this instant. Take moment of inertia about the bottom contact of sphere as (7/5)mR 2 : (A)
9.
(C)
A three dimensional vector has equal magnitude in all th ree direction. The magnitude of this vector is 30. Find the magnitude of component in each direction : (A) 5 2
8.
50 61 , 17 17
0
v0
2
PG Brainstormer - 8C 14.
15.
A sphere cannot roll continuously on : (A) a smooth horizontal surface. (C) a rough horizontal surface.
A cylinder of mass ‘ M ’' and radius r is rolling without slipping on a horizontal surface. The velocity of its C.M. is equal to v. The total angular momentum of the cylinder about a point P at distance R/2 from centre of cylinder is : (A)
2
MR
4
(C) MR 2
16.
(B)
MR
2
P R/2 v
2
(D) Zero
Y X A L A G S C I S Y H P
A solid sphere of mass M and radius R is lying on a rough h orizontal plane. A constant force F = 4 Mg acts vertically at point P such that OP makes 60º with horizontal. Find the minimum value of coefficient of friction µ so that sph ere starts pure rolling : (A) (C)
17.
(B) a smooth inclined surface. (D) a rough inclined surface.
3
(B)
7 2
(D)
7
F =
4Mg
P
4
60º
O
7
2 5
STATEMENT-1: A sphere rolls down a rough inclined plane without sliding. It gains rotational K.E. due to the work
done by friction. becau se
STATEMENT-2: As the force of friction is static, n et work done by friction is zero.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True. 18.
A rectangular block has a square base measuring a × a, and its height is h. It moves on a horizontal surface in a direction perpendicular to one of the edges on the base. If no external force is acting on the block find the coefficient of friction is µ if it topples : (A) µ > h/a
19.
(C) µ >
2a h
(D) µ >
a
2h
A uniform rod of length 2 l is placed with one end in contact with the horizontal table and is then inclined at an angle to the horizontal and allowed to fall. Friction is sufficient so that the end in contact does not slip. When it becomes horizontal, its angular velocity will be : (A) =
20.
(B) µ > a/h
3 g sin 2l
(B) =
2l 3 g sin
(C) =
g sin l
(D) =
l g sin
A rod of uniform density and length l is hinged at O and kept at horizontal frictionless surface. An impulse P0 ( 130 kg-m/s) along the surface is applied on rod as shown in the figure. The impulse on the rod due to hinge just
after application of P0 in kg-m/s is [tan = 9/7] (A) (C)
65 85
(B)
(D)
75
O
95
*
PHYSICS
l/2
*
*
*
C
l/4
P0
*
3
PG Brainstormer - 8C
PG Brainstormer - 8 C RIGID BODY DYNAMICS & CONSERVATION LAWS
An Ultimate Tool to understand advanced High School Physics
Time Allow ed
by ASHISH ARORASir
M aximum M arks
60 M in 60
Y X A L A G S C I S Y H P
OMR Sheet for the PG Brainstormer - 8C (MECHANICS) A
PHYSICS
B
C
D
A
1
11
2
12
3
13
4
14
5
15
6
16
7
17
8
18
9
19
10
20
B
C
D
4
PG Brainstormer - 8C
PG Brainstormer - 8 C RIGID BODY DYNAMICS & CONSERVATION LAWS
An Ultimate Tool to understand advanced High School Physics
