1
IIT-JEE 2012 Paper 1 Offline
+3
-1

A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at t = 0. It then executes simple harmonic motion with angular frequency $$\omega$$ = ($$\pi$$/3) rad/s. Simultaneously, at t = 0, a small pebble is projected with speed v from point P at an angle of 45$$^\circ$$ as shown in the figure. Point O is at a horizontal distance of 10 m from O. If the pebble hits the block at t = 1 s, the value of v is (take g = 10 m/s2)

A
$$\sqrt {50}$$ m/s
B
$$\sqrt {51}$$ m/s
C
$$\sqrt {52}$$ m/s
D
$$\sqrt {53}$$ m/s
2
IIT-JEE 2012 Paper 1 Offline
+3
-1

Young's double slit experiment is carried out by using green, red and blue light, one colour at a time. The fringe widths recorded are $$\beta$$G, $$\beta$$R and $$\beta$$B, respectively. Then,

A
$$\beta$$G > $$\beta$$B > $$\beta$$R
B
$$\beta$$B > $$\beta$$G > $$\beta$$R
C
$$\beta$$R > $$\beta$$B > $$\beta$$G
D
$$\beta$$R > $$\beta$$G > $$\beta$$B
3
IIT-JEE 2012 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

Consider the motion of a positive point charge in a region, there are simultaneous uniform electric and magnetic fields $$\overrightarrow E = {E_0}\widehat j$$ and $$\overrightarrow B = {B_0}\widehat j$$. At time t = 0, this charge has velocity $$\overrightarrow v$$ in the xy-plane, making an angle $$\theta$$ with the x-axis. Which of the following option(s) is(are) correct for time t > 0 ?

A
If $$\theta$$ = 0$$^\circ$$, the charge moves in a circular path in the xy-plane.
B
If $$\theta$$ = 0$$^\circ$$, the charge undergoes helical motion with constant pitch along the y-axis.
C
If $$\theta$$ = 10$$^\circ$$, the charge undergoes helical motion with its pitch increasing with time, along the y-axis.
D
If $$\theta$$ = 90$$^\circ$$, the charge undergoes linear but accelerated motion along the y-axis.
4
IIT-JEE 2012 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

A person blows into the open end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,

A
a high-pressure pulse starts travelling up the pipe, if the other end of the pipe is open.
B
a low-pressure pulse starts travelling up the pipe, it the other end of the pipe is open.
C
a low-pressure pulse starts travelling up the pipe, if the other end of the pipe is closed.
D
a high-pressure pulse starts travelling up the pipe, if the other end of the pipe is closed.
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