1
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x0. Consider two cases:
(i) when the block is at x0; and
(ii) when the block is at x = x0 + A.
In both cases, a particle with mass m( < M) is softly placed on the block after which they stick on each other. Which of the following statement(s) is(are) true about the motion after the mass m is placed on the mass M?
A
The amplitude of oscillation in the first case changes by a factor of $$\sqrt {{M \over {m + M}}}$$, whereas in the second case it remains unchanged.
B
The final time period of oscillation in both the cases is same
C
The total energy decreases in both the cases
D
The instantaneous speed at x0 of the combined masses decreases in both the cases
2
JEE Advanced 2015 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Two independent harmonic oscillators of equal masses are oscillating about the origin with angular frequencies $$\omega$$1 and $$\omega$$2 and have total energies E1 and E2, respectively. The variations of their momenta p with positions x are shown in the figures. If $${a \over b} = {n^2}$$ and $${a \over R} = n$$, then the correct equations is/are
A
E1$$\omega$$1 = E2$$\omega$$2
B
$${{{\omega _2}} \over {{\omega _1}}} = {n^2}$$
C
$${\omega _1}{\omega _2} = {n^2}$$
D
$${{{E_1}} \over {{\omega _1}}} = {{{E_2}} \over {{\omega _2}}}$$
3
IIT-JEE 2009 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2

A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance. Then,

A
the intensity of the sound heard at the first resonance was more than that at the second resonance.
B
the prongs of the tuning fork were kept in a horizontal plane above the resonance tube.
C
the amplitude of vibration of the ends of the prongs is typically around 1 cm.
D
the length of the air-column at the first resonance was somewhat shorter than 1/4th of the wavelength of the sound in air.
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