1
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is -
A
$${{4\pi } \over 3}$$
B
$${3 \over 8}\pi$$
C
$${7 \over 3}\pi$$
D
$${{8\pi } \over 3}$$
2
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be :
A
$${A \over 2}$$
B
$${A \over {2\sqrt 2 }}$$
C
$${A \over {\sqrt 2 }}$$
D
A
3
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance 'L/2' from its centre on both sides, it reduces the oscillation frequency by 20%. The value of radio m/M is close to :
A
0.77
B
0.57
C
0.37
D
0.17
4
JEE Main 2018 (Online) 16th April Morning Slot
+4
-1
An oscillator of mass M is at rest in its equilibrium position in a potential
V = $${1 \over 2}$$ k(x $$-$$ X)2. A particle of mass m comes from right with speed u and collides completely inelastically with M and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after 13 collisions is : (M = 10, m = 5, u = 1, k = 1)
A
$${1 \over {\sqrt 3 }}$$
B
$${1 \over 2}$$
C
$${2 \over 3}$$
D
$${3 \over {\sqrt 5 }}$$
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