HARD
Earn 100

Two identical cubes A and B of same mass 2m and side 2d are placed one over the other as shown in figure. B is attached to one end of a spring of force constant k. The other end of the spring is attached to a wall. The system is resting on a smooth horizontal surface with the spring in the relaxed state. A small object of mass m moving horizontally with speed v at a height d above the horizontal surface hits elastically the block B along the line of their centre of mass. There is no friction between A and B :

(a) find the minimum value of v(say v0) such that block A will topple over block B

(b) if v=v02 find the amplitude of oscillation of block spring system.

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Important Questions on Rotational Motion

MEDIUM

A 34 m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If Ff and Fw are the reaction forces of the floor and the wall, then ratio of FwFf will be :
(Use g=10 m s-2.)

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MEDIUM

Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is off mass 'm' and has another weight of mass 2 m hung at a distance of 75 cm from A. The tension in the string at A is:

 

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HARD

One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge at point O. A block of weight αW is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of  22W. Which of the following statement(s) is(are) correct?

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HARD
An L -shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB=BC, and the angle made by AB with downward vertical is θ, then:
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HARD
A uniform wooden stick of mass 1.6 kg and length l rests in an inclined manner on a smooth, vertical wall of height h <l such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of 30o with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio hl and the frictional force f at the bottom of the stick are: g=10 m s-2
MEDIUM
A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10.0 cm mark the scale is found to be balanced at 40.0 cm mark. The mass of the metre scale is found to be x×10-2 kg. The value of x is _____ .
EASY

A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass m is suspended from the rod at 160 cm mark as shown in the figure. Find the value of m such that the rod is in equilibrium. (g=10 m s-2

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MEDIUM
A uniform rod AB is suspended from a point X, at a variable distance x from A, as shown. To make the rod horizontal, a mass m is suspended from its end A. A set of (m, x) value is recorded. The appropriate variables that give a straight line, when plotted, are:

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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:
EASY
In a physical balance working on the principle of moments, when 5mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?
MEDIUM

A bead of mass m stays at point Pa, b on a wire bent in the shape of a parabola y=Cx2 and rotating with angular speed ω (see figure). The value of ω is (neglect friction)

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HARD

A football of radius R is kept on a hole of radius r(r<R) made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle θ from the horizontal as shown in the figure below. The maximum value of θ  so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale)

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MEDIUM
A cube of side'a'is placed on an inclined plane of inclination θ. What is the maximum value of θ for which cube will not topple?
HARD

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Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is μ=0.4 , the maximum possible value of 100×ba for a box not to topple before moving is ________

HARD
A cubical block of side L rests on a rough horizontal surface with coefficient of friction μ. A horizontal force F is applied on the block as shown. If the coefficient of friction is sufficiently high, so that the block does not slide before toppling, the minimum force required to topple the block is

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MEDIUM

A bullet of mass m moving with a speed ν hits a stationary block of mass M at the topmost point and gets embedded in it. If friction is sufficient to prevent slipping then the block.

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HARD

Find the greatest height at which force F may be applied to slide the block without tipping over.

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HARD

A uniform solid sphere of radius R is rolling without sliding on a horizontal surface with a velocity v0. It collides with an obstacle of height h (< R) inelastically. Find the angular speed of the sphere just after the collision.

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MEDIUM

Represent the union of two sets by Venn diagram for each of the following.

X={x | x is a prime number between 80 and 100}

Y={y | y is an odd number between 90 and 100}

EASY
In the case of toppling of the body about the point A. (Shown in the figure)

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