HARD
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The system shown adjacent is in equilibrium. Blocks A,B & C are of equal masses m (Assume springs to be ideal).

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Then choose the correct statements.

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Important Questions on Laws of Motion

MEDIUM
A stream of water flowing horizontally with a speed of 15 ms-1 gushes out of a tube of cross-sectional area 10-2 m2 and hits a vertical wall nearby. The force exerted on the wall by the impact of water (assuming it does not rebound) is
EASY

A mass m is attached to two springs as shown in figure. The spring constants of two springs are K1 and K2. For the frictionless surface, the time period of oscillation of mass m is

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HARD
A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x - axis. Its kinetic energy changes with time as dKdt=γt, where γ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?
MEDIUM
An elevator of mass m  is connected to a rope which pulls the elevator up with a maximum acceleration equal to a . If the maximum bearable tension in the rope is T , then for a safe journey the minimum diameter of the rope is [ g = acceleration due to gravity]
HARD
System shown in the figure is in equilibrium and at rest. The spring and string are massless, now the string is cut. The acceleration of mass 2m and m just after the string is cut will be
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EASY
Three blocks A, B and C, of masses 4 kg, 2 kg 1 kg and respectively, are in contact on a frictionless surface, as shown. If a force of 14 N  is applied on the 4 kg block, then the contact force between A and B is:

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MEDIUM
A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of 45° at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is g=10 m s-2
MEDIUM
Two masses m1=5 kg and m2=10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m2 to stop the motion is:

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MEDIUM

Two identical springs are connected to mass m as shown  (k=spring constant) . If the period of the configuration in (i) is 2 s, the period of the configuration (ii) is:

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MEDIUM
One end of a massless spring of spring constant k and natural length l0 is fixed while the other end is connected to a small object of mass m lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity ω about an axis passing trough fixed end, then the elongation of the spring will be
HARD

The machine as shown has 2 rods of length 1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has roller that rolls along the floor in a slot. As the roller goes back and forth, a 2 kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a :

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EASY
A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is k. If now they are connected in parallel and force constant is k, then k' : k'' is
MEDIUM
Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively
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MEDIUM
A rod of weight W is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance d from each other. The centre of mass of the rod is at distance x from A . the normal reaction on A is:
HARD
On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r << R, and the surface tension of water is T, value of r just before bubbles detatch is :
(density of water is ρ w )

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MEDIUM
A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis will be  g=10  m s-2,
HARD
A particle of mass m is acted upon by a force F given by the empirical law F=Rt2 vt. If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot
EASY

As shown in the figure, an iron block A of volume 0.25 m3 is attached to a spring S of unstretched length 1.0 m and hanging to the ceiling of a roof. The spring gets stretched by 0.2 m. This block is removed and another block B of iron of volume 0.75 m3 is now attached to the same spring and kept on a frictionless incline plane of 30° inclination. The distance of the block from the top along the incline at equilibrium is

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MEDIUM

A block of mass 20 kg is suspended through two spring balances with negligible mass as shown in figure. What will be the readings in the upper and lower balance respectively ?

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MEDIUM
1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to a 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is