JEST Question 2009[1]

TRAJECTORY.IN The Everything of  IIT JAM, MCA, GATE, NET,  University Education, Science Career  JEST – 2009(Memory based) Q. 1 A cylinder of mass M and radius R is made of material with radially dependent density f(r) = krn. It starts from rest and rolls without slipping down an inclined plane of height (vertical) H at the bottom of the inclined plane, its translation speed is (a) 1

(b) 2

(c) 3

8 gH . Based on this n = – ? 7 (d) 4

Q. 2. Point mass slides down (without function) on a rigid sphere of radius R. If the angle with the vertical axis when the point mass starts sliding is θo, the angle at which the point mass leaves the surface of the sphere is

⎛2 ⎞ (a) sin –1 ⎜ cos θ o ⎟ ⎝3 ⎠

⎛1 ⎞ (b) tan –1 ⎜ cos θ o ⎟ 2 ⎝2 ⎠

⎛2 ⎞ (c) cos –1 ⎜ cos θ o ⎟ ⎝3 ⎠

⎛1 ⎞ (d) cos –1 ⎜ tan θ o ⎟ 4 ⎝3 ⎠

Q. 3. When a metal lattices recrystallizes from FCC → BCC then it is observed that there is no change of volume, if d is the nearest neighbor distance then what will the ratio

d fc d bc

=?

Q. 4. A sphere of mass M and radius R has a men uniform density distribution given by

ρ (r ) = ρo cos θ (in spherical polar coordinates). The gravitational potential of this sphere at a point close to but not on its surface has (a) non zero dipole and monopole moment. (b) non zero dipole moment but zero monopole moment (c) non zero monopole but zero dipole moment (d) has zero but dipole and monopole moment

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TRAJECTORY.IN The Everything of  IIT JAM, MCA, GATE, NET,  University Education, Science Career  Q. 5.

y=

1

x

 

y=

1

x

is revolved around x axis to make a convolution of evolution the ratio of base are A to

the volume v of rev. of convolution us

A =? V

Q. 6. A proton moving along +ve x axis with γ =

1 1 – v2 / c2

= γ A collide with another proton

at rest. It two protons continue to move with equal magnitudes of momentum along the same after the collision, what is final γ for each proton? 7. Particles moving in 1 – d potential well v( x) = α x, α > 0 (confined to region x > 0) system in a thermal bath at temperature T, find mean thermal energy of particle.

G G G G G kG 8. The Runge lenz vector n = r × l – r (k const l = r × r , angular momentum) us a constant r of motion, the potential V(r) varies with r as (a)

k

(b)

r

(c) kr 2

k

r2

(d) should be non central in nature

9. In equilibrium there can be no free charge inside a metal. If we forcibly put change in the interior, then the time taken by the charge to move to the surface (if the r = 108 ( – 2m ) ) –1

(1) 1see

(b) 10–4 see

(c) 10–8 sec

(d) 10–19 see

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TRAJECTORY.IN The Everything of  IIT JAM, MCA, GATE, NET,  University Education, Science Career  10. If H =

Px2 + Py2 2m

+

1 mω 2 ( x 2 + y 2 + 2 xy ) then the ground state energy of the quantum state 2

will be (b) = ω

(a) 0

(c)

1 =ω 2

(d)

1 =ω 2

11. A classical particle of mass on is constrained to move on a plane along a curve, expressed as r =

(

)

k , of particle = υ iˆ + ˆj . The ratio of angular momentum to linear cos (θ + π / 4 )

momentum in (a) r / 2

(b) r 2

(c) k / 2

(d) k 2

12. Find electric field at the circumcenter of a regular pentagon where charge θ are placed at vertices and one of side is along x axis and circumcenter lying on y axis. 13. Hamiltonian and parity.

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