IIT-JEE Exam

A proton is fired from very far away towards a nucleus with charge Q = 120 e, where e is the electronic charge.
It makes a closest approach of 10 fm to the nucleus. The de Brogle wavelength (in units of fm) of the proton at
its start is

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IIT-JEE Other Question

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and
magnetic fields j E  E0

and j B  B0

. At time t = 0, this charge has velocity v
 in the x-y plane, making an
angle  with x-axis. Which of the following option(s) is(are) correct for time t > 0 ?
(A) If  = 0°, the charge moves in a circular path in the x-z plane.
(B) If  = 0°, the charge undergoes helical motion with constant pitch along the y-axis.
(C) If  = 10°, the charge undergoes helical motion with its pitch increasing with time, along the y-axis.
(D) If  = 90°, the charge undergoes linear but accelerated motion along the y-axis. A lamina is made by removing a small disc of diameter 2R froma bigger disc of uniform mass density and radius
2R, as shown in the figure. The moment of inertia of this lamina about axes passing through O and P is IO and
IP, respectively. Both these axes are perpendicular to the plane of the lamina. The ratio
Ip/Io
to the nearest integer
is :