1
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A block $$M$$ hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to fixed rigid support at $$O.$$ A transverse wave pulse (Pulse 1) of wavelength $${\lambda _0}$$ is produced at point $$O$$ on the rope. The pulse takes time $${T_{OA}}$$ to reach point $$A.$$ If the wave pulse of wavelength $${\lambda _0}$$ is produced at point $$A$$ (Pulse 2) without disturbing the position of $$M$$ it takes time $${T_{AO}}$$ to reach point $$O.$$ which of the following options is/are correct?

A
The time $${T_{AO}} = {T_{OA}}$$
B
The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the midpoint of rope
C
The wavelength of Pulse 1 becomes longer when it reaches point $$A$$
D
The velocity of any pulse along the rope is independent of its frequency and wavelength
2
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A block of mass $$M$$ has a circular cut with a frictionless surface as shown. The block resets on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at $$x=0,$$ in a co-ordinate system fixed to the table. A point mass $$m$$ is released from rest at the topmost point of the path as shown and it slides down.

When the mass loses contact with the block, its position is $$x$$ and the velocity is $$v.$$ At that instant, which of the following options is/are correct?

A
The position of the point mass $$m$$ is :

$$x = - \sqrt 2 {{mR} \over {M + m}}$$
B
The velocity of the point mass $$m$$ is :

$$v = \sqrt {{{2gR} \over {1 + {m \over M}}}}$$
C
The $$x$$ component of displacement of the center

of mass of the block $$M$$ is: $$- {{mR} \over {M + m}}$$
D
The velocity of the block $$M$$ is:

$$V = - {m \over M}\sqrt {2gR}$$
3
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
A human body has a surface area of approximately $$1\,m{}^2.$$ The normal body temperature is $$10$$ $$K$$ above the surrounding room temperature $${T_0}.$$ Take the room temperature to be $${T_0} = 300K.$$ For $${T_0} = 300\,K,$$ the value of $$\sigma T_0^4 = 460\,W{m^{ - 2}}$$ (where $$\sigma$$ is the Stefan-Boltzmann constant).

Which of the following options is / are correct?
A
The amount of energy radiated by the body in $$1$$ second is close to $$60$$ joules
B
If the surrounding temperature reduces by a small amount $$\Delta {T_0} < < {T_0},$$ then to maintain the same body temperature the same (living) human being needs to radiate $$\Delta W = 4\sigma T_0^3\Delta {T_0}$$ more energy per unit time
C
Reducing the exposed surface area of the body (e.g. by curling up) allows human to maintain the same body temperature while reducing the energy lost by radiation
D
If the body temperature rises significantly then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths
4
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A circular insulated copper wire loop is twisted to form two loops of area $$A$$ and $$2A$$ as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field $$\overrightarrow B$$ points into the plane of the paper. At $$t=0,$$ the loop starts rotating about the common diameter as axis with a constant angular velocity $$\omega$$ in the magnetic field.

Which of the following options is/are correct?

A
The emf induced in the loop is proportional to the sum of the areas of the two loops
B
The amplitude of the maximum net emf induced due to both the loops is equal to the amplitude if maximum emf induced in the smaller loop alone
C
The net emf induced due to both the loops is proportional to $$\cos \,\omega t$$
D
The rate of change of the flux is maximum when the plane of the loops is perpendicular to plane of the paper
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