1
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1
Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and I, respectively. At time t = 0 one particle has displacement A while the other one has displacement $${{ - A} \over 2}$$ and they are moving towards each other. If they cross each other at time t, then t is :
A
$${T \over 6}$$
B
$${5T \over 6}$$
C
$${T \over 3}$$
D
$${T \over 4}$$
2
JEE Main 2016 (Offline)
+4
-1
A particle performs simple harmonic motion with amplitude $$A.$$ Its speed is trebled at the instant that it is at a distance $${{2A} \over 3}$$ from equilibrium position. The new amplitude of the motion is:
A
$$A\sqrt 3$$
B
$${{7A} \over 3}$$
C
$${A \over 3}\sqrt {41}$$
D
$$3A$$
3
JEE Main 2015 (Offline)
+4
-1
The period of oscillation of a simple pendulum is $$T = 2\pi \sqrt {{L \over g}}$$. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using wrist watch of 1 s resolution. The accuracy in the determination of g is:
A
1 %
B
5 %
C
2 %
D
3 %
4
JEE Main 2015 (Offline)
+4
-1
A pendulum made of a uniform wire of cross sectional area $$A$$ has time period $$T.$$ When an additional mass $$M$$ is added to its bob, the time period changes to $${T_{M.}}$$ If the Young's modulus of the material of the wire is $$Y$$ then $${1 \over Y}$$ is equal to :
($$g=$$ $$gravitational$$ $$acceleration$$)
A
$$\left[ {1 - {{\left( {{{{T_M}} \over T}} \right)}^2}} \right]{A \over {Mg}}$$
B
$$\left[ {1 - {{\left( {{T \over {{T_M}}}} \right)}^2}} \right]{A \over {Mg}}$$
C
$$\left[ {{{\left( {{{{T_M}} \over T}} \right)}^2} - 1} \right]{A \over {Mg}}$$
D
$$\left[ {{{\left( {{{{T_M}} \over T}} \right)}^2} - 1} \right]{{Mg} \over A}$$
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