CLASS TEST
PHYSICS CLASS TEST # 46
SECTION-I
Single Correct Answer Type 6 Q. [3 M (–1)]
1. A uniform circular disc has a moment of inertia I and radius of gyration K about an axis perpendicular to the
disc and passing through its centre. A smaller concentric disc is taken out from this bigger disc. As a result of
which moment of inertia and radius of gyration of the resulting body about the same axis :-
(A) Increases and decreases respectively (B) Increases and increases respectively
(C) Decreases and increases respectively (D) Decreases and decreases respectively
2. A uniform ladder of length 2L and mass m leans against a wall in a vertical plane at an angle to the horizontal.
The floor is rough, having a coefficient of static friction µ. A person of mass M stands on the ladder at a distance
D from its base (see figure). If the wall is frictionless, the maximum distance (Dmax) up the ladder that the person
can reach before the ladder slips is :
/////////////////////////////////////
2L
D
//////////////////////////////////////////// µ
m
(A) µL tan (B) 2L tan
M
m m m
(C) 2 1 M tan M L (D) 2L 1 tan
M
3. A uniform rod of mass ‘m’ and length ‘2l’ is balanced on triangular prism. Now length of rod is cut from
2
one end and placed over the shortened part such that the ends meet. The initial angular acceleration is
3g 2g 3g 5g
(A) (B) (C) (D)
5 3 7 7
4. The moment of inertia of a cube of mass m and side a about the diagonal of one of it's face is :-
ma 2 ma 2 5ma 2 2ma 2
(A) (B) (C) (D)
12 6 12 3
5. A uniform square plate is folded from one of its corner as shown in figure. The moment of inertia about the xx'
axis is then (xx' axis is perpendicular to plane of square plate and passes through centre) :-
(A) Increased (B) The same
(C) Decreased (D) Changed in unpredicted manner
x' x'
x x
initially finally
6. A uniform thin wire of length 3L and mass 3M is bent into the form of an equilateral triangle ABC as shown in
figure. The moment of inertia of the system about the median AM is :-
30° 30°
60° 60°
B M C
ML2 ML2 ML2 2
(A) (B) (C) (D) ML2
4 12 6 3
Multiple Correct Answer Type 5 Q. [4 M (–1)]
7. A man weighing W stands on a horizontal beam (hinged on a wall) of negligible weight at point C and holds a
massless rope passing over two smooth pulleys. The rope is attached to point B on the beam as shown. If the
system is in equilibrium, then :-
A
B C
2m
2m
(A) If W = 600 N, tension in string is 400 N
(B) If W = 600 N hinge force at A is 200 N
(C) Hinge force at A is always in vertically downward direction, irrespective of value of W
(D) Hinge force at A is always in vertically upward direction, irrespective of value of W
8. An eccentric cylinder used in vibrator has a mass of 18 kg and rotates about an axis 50 mm from its geometric
centre and perpendicular to the top view as shown in diagram. If the magnitude of and are 10 rad/s and
2 rad/s2 respectively at the instant shown, then choose the CORRECT option(s) :- (The whole system is
kept in gravity free region)
x
Hinge
O
m
0 m 50mm
15
y
Top view
(A) Magnitude of x-component of hinge force is 90 N
(B) Magnitude of y-component of hinge force is 1.8 N
(C) Net torque required about the hinge is 0.495 N-m
(D) Net hinge force has positive x & y component.
9. Two beads of mass m1 and m2 are connected by a light rigid rod. System is at rest placed between a smooth
wall and a rough floor having coefficient of friction . Which of the following are correct. (T is the force
exerted by the rod, N1 is the normal force exerted by the wall, N2 is the normal force exerted by the ground
and f is the friction force exerted by the ground.)
m1
Ro
d
m2
2 m
(A) Minimum value of so that system does not slip is cot–1 1 m
1
(B) N1 = Tcos (C) N2 = (m1 + m2)g (D) f = Tcos
10. A rigid body is observed in equilibrium in a particular non rotating, non inertial frame. What can you conclude,
if the body is observed from an inertial frame.
(A) The body is in rotational equilibrium but not in translational equilibrium
(B) Net torque of all the forces on body about its centre of mass is a null vector.
(C) Net torque of all the forces on the body about any point that is collinear with line of acceleration of mass
centre is a null vector.
(D) Net torque of all the forces on the body about all point on a line that is parallel to the line of
acceleration of mass centre is a null vector.
11. Find the moment of inertia (in kg-m2) of a semicircular plane of radius 1 m and mass 1 kg as shown. Given sin
= 3/32.
X’
15 32 2
(A) IXX' = 0.5 kg m2 (B) IXX' = 0.25 kg m2 (C) IAB = 1 kg m2 (D) IAB kgm
12
Matrix List Type (4 × 4 × 4) (1 Table × 3Q.) [3(–1)]
(Single options correct) (Three Columns and Four Rows)
Answer Q.12, Q.13 and Q.14 by appropriately matching the information given in the three columns
of the following table. Radius of each object is R.
Column–1 Column-2 Column-3
Object of mass m Position of Radius of gyration
centre of mass
from ground
C
5R 2
(I) solid sphere (i) (P) R
8 5
C
semispherical
shell R 2
(II) (ii) (Q) R
2 3
C
half ring 4R R
(III) (iii) R – (R)
3 2
C
half disc 2R R
(IV) (iv) R – (S)
2
12. Which of the following body has farthest centre of mass from C, what is its distance of centre of mass
from ground & its radius of gyration about vertical axis passing through 'C' :-
(A) (III) (iv) (R) (B) (II) (ii) (Q) (C) (I) (iii) (P) (D) (IV) (i) (S)
13. Which of the following body has nearest centre of mass from C. What is its distance of centre of mass from
ground and its radius of gviration about vertical line passing through C :-
(A) (II) (iii) (S) (B) (I) (i) (P) (C) (IV) (ii) (R) (D) (III) (iv) (Q)
14. A body having maximum moment of inertia about vertical line passing through 'C', what is its distance of
centre of mass from ground and its radius of gyration about vertical line passing through C.
(A) (II) (ii) (Q) (B) (I) (iii) (S) (C) (III) (iv) (R) (D) (IV) (i) (P)
SECTION-IV
Numerical Grid Type (Single digit Ranging from 0 to 9) 4 Q. [4 M(0)]
1. A thin rod of total length l and of mass m has variable linear density given by = 0[1 + (x/l)], where x is the
distance from one end. Calculate the moment of inertia (in kg m2) about an axis perpendicular to the length of
the rod and passing midway, at x = l/2. (Take = 1 kg/m, l = 2m)
2. The moment of inertia of the plate in fig(a) about the about axis shown is I. The moment of inertia of the
hexagonal plate of same material shown in figure(b) about the axis given in figure(b) is 10 I,find value of .
a a
a
Fig(a) Fig(b)
3. Half ring of mass m and radius R is released from the position shown in diagram. A small point mass of same
2g
mass is also fixed at the end as shown in figure. If the initial acceleration of point mass m is then find the
value of
4. The drawing shows the top view of two doors. The doors are uniform and identical. Door A rotates about an
axis through its left edge, while door B rotates about an axis through the center. The same force F is applied
perpendicular to each door at its right edge and the force remains perpendicular as the door turns. Starting
3n
from rest, door A rotates through a certain angle in 3 s. If door B takes sec to rotate through the same
2
angle. Fill the value of 'n' in OMR sheet.
F
Axis
Door A
F
Axis
Door B
