A block of mass 2M is attached to a massless spring with spring-constant k.This block is connected to two other blocks of masses M and 2M using two massless pulleys and strings. The accelerations of the blocks are a1, a2 and a3 as shown in the figure. The system is released from rest with the spring in its unstretched state. The maximum extension of the spring is x0. Which of the following option(s) is/are correct? [g is the acceleration due to gravity. Neglect friction]
A
$${a_2} - {a_1} = {a_1} - {a_3}$$
B
At an extension of $${{{x_0}} \over 4}$$ of the spring, the magnitude of acceleration of the block connected to the spring is $${{3g} \over {10}}$$.
C
$${x_0} = {{4Mg} \over k}$$
D
When spring achieves an extension of $${{{x_0}} \over 2}$$ for the first time, the speed of the block connected to the spring is $$3g\sqrt {{M \over {5k}}} $$
2
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+3
-0
In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle $$\theta$$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $$\mu$$1 and that between the floor and the ladder is $$\mu$$2. The normal reaction of the wall on the ladder is N1 and that of the floor is N2. If the ladder is about to slip, then
A small block of mass 0.1 kg lies on a fixed inclined plane PQ which makes an angle $$\theta$$ with the horizontal. A horizontal force of 1 N acts on the block through its centre of mass as shown in the figure. The block remains stationary if (take g = 10 m/s2)
A
$$\theta$$ = 45$$^\circ$$
B
$$\theta$$ > 45$$^\circ$$ and a frictional force ats on the block towards P.
C
$$\theta$$ > 45$$^\circ$$ and a frictional force ats on the block towards Q.
D
$$\theta$$ < 45$$^\circ$$ and a frictional force ats on the block towards Q.
4
IIT-JEE 1986
MCQ (More than One Correct Answer)
+2
-0.5
A reference frame attached to the earth
A
is an inertial frame by definition
B
cannot be an inertial frame because the earth is revolving around the sun
C
is an inertial frame because Newton's laws are applicable in this frame
D
cannot be an inertial frame because the earth rotating about its own axis
