Question19:-Orthogonal property of Legender’s polynomial is given by
t_-1*1°*Pm(x)Pn(x)=0° m#n
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t_O* 1° * P(x) Pr(x)=0°' men
it_O“1**Pm(x)Pn(x)=0° men

Correct Answer:- Option-A
Question20:-Find the value of ** *|~(5/2)’ i.e gamma (5/2)
8: (3sqrt(pi))/(4)°
(sqrt(pi))/(2)°
(15sqrt(pi))/(8)*

:-` (sqrt(pi))/(3)°

Correct Answer:- Option-A
Question21:-A particle of mass m is bound by a linear potential U=kr. For what energy will the orbit be a circle of radius r
about the origin

2: (௮௮/2:

B:-3kr

C:-kr

D:-* (kr)/(2)°

Correct Answer:- Option-A
Question22:-Two circular discs have the same mass m and same thickness t. Disc one has uniform density less than that of
disc two. Which of the following is correct.

A:-Disc two has larger moment of inertia

B:-Disc one has larger moment of inertia

C:-Both have same moment of inertia

D:-Can not be predicted from given data.

Correct Answer:- Option-B
Question23:-Consider motion of a particle of mass m under the influence of a force F=-kr, where k is a positive constant and
ris the position vector of the particle. Now the orbit will be

A:-Ellipse

B:-Along a line

C:-Circle

D:-Parabola

Correct Answer:- Option-A
Question24:-A violin string 0.5m long has a fundamental frequency 200Hz. At what speed does a transverse pulse travel on
this string?

A:-100m/s

B:-400m/s

C:-200m/s

D:-300m/s

Correct Answer:- Option-C
Question25:-Consider the longitudinal vibration of a linear triatomic molecule with two atoms of mass m each symmetrically
situated on either sides of an atom of mass M. Now which of the following is a normal mode frequency of the system, if we
use a spring model

A:-sqrt(kM)*

D:-sqrt(kMm)*

Correct Answer:- Option-C
Question26:-Number of generalized coordinates required to describe the motion of a particle of mass m constrained to
move on the surface of a sphere of radius R are
-3

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sl
:-0
D:-2
Correct Answer:- Option-D
Question27:-The Hamiltonian of a particle in a central potential V(r) is
~` (0^ (2))/(2)`
(0^ (2))/(2ा1)` +\/(1)
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A
B
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