1
JEE Advanced 2013 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

A point charge Q is moving in a circular orbit of radius R in the xy-plane with an angular velocity $$\omega$$. This can be considered as equivalent to a loop carrying a steady current $${{Q\omega } \over {2\pi }}$$. A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant $$\gamma$$.

The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is
A
$${{BR} \over 4}$$
B
$${{BR} \over 2}$$
C
BR
D
2BR
2
JEE Advanced 2013 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

A point charge Q is moving in a circular orbit of radius R in the xy-plane with an angular velocity $$\omega$$. This can be considered as equivalent to a loop carrying a steady current $${{Q\omega } \over {2\pi }}$$. A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant $$\gamma$$.

The change in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is

A
$$ - \gamma BQ{R^2}$$
B
$$ - \gamma {{BQ{R^2}} \over 2}$$
C
$$\gamma {{BQ{R^2}} \over 2}$$
D
$$\gamma BQ{R^2}$$
3
JEE Advanced 2013 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

The mass of a nucleus $$_Z^AX$$ is less than the sum of the masses of (A-Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of masses m1 and m2 only if (m1 + m2) < M. Also two light nuclei of masses m3 and m4 can undergo complete fusion and form a heavy nucleus of mass M' only if (m3 + m4) > M'. The masses of some neutral atoms are given in the table below :

$$_1^1H$$ 1.007825 u $$_1^2H$$ 2.014102 u
$$_3^6Li$$ 6.015123 u $$_3^7Li$$ 7.016004 u
$$_{64}^{152}Gd$$ 151.919803 u $$_{82}^{206}Pb$$ 205.974455 u
$$_1^3H$$ 3.016050 u $$_2^4He$$ 4.002603 u
$$_{30}^{70}Zn$$ 69.925325 u $$_{34}^{82}Se$$ 81.916709 u
$$_{83}^{209}Bi$$ 208.980388 u $$_{84}^{210}Po$$ 209.982876 u

(1 u = 932 MeV/c2)

The correct statement is

A
the nucleus $$_3^6Li$$ can emit an alpha particle.
B
the nucleus $$_{84}^{210}Po$$ can emit a proton.
C
deuteron and alpha particle can undergo complete fusion.
D
the nuclei $$_{30}^{70}Zn$$ and $$_{34}^{82}Se$$ can undergo complete fusion.
4
JEE Advanced 2013 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

The mass of a nucleus $$_Z^AX$$ is less than the sum of the masses of (A-Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of masses m1 and m2 only if (m1 + m2) < M. Also two light nuclei of masses m3 and m4 can undergo complete fusion and form a heavy nucleus of mass M' only if (m3 + m4) > M'. The masses of some neutral atoms are given in the table below :

$$_1^1H$$ 1.007825 u $$_1^2H$$ 2.014102 u
$$_3^6Li$$ 6.015123 u $$_3^7Li$$ 7.016004 u
$$_{64}^{152}Gd$$ 151.919803 u $$_{82}^{206}Pb$$ 205.974455 u
$$_1^3H$$ 3.016050 u $$_2^4He$$ 4.002603 u
$$_{30}^{70}Zn$$ 69.925325 u $$_{34}^{82}Se$$ 81.916709 u
$$_{83}^{209}Bi$$ 208.980388 u $$_{84}^{210}Po$$ 209.982876 u

(1 u = 932 MeV/c2)

The kinetic energy (in keV) of the alpha particle, when the nucleus $$_{84}^{210}Po$$ at rest undergoes alpha decay, is

A
5319
B
5422
C
5707
D
5818
JEE Advanced Papers
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12