EASY
Earn 100

Differentiate between centre of mass and centre of gravity.

Important Questions on Laws of Motion

MEDIUM
A man weighing 70 kg is riding on a cart of mass 30 kg which moves along a level floor at a speed of 3 m s-1. If he runs on the cart so that his velocity relative to the cart is 4 m s-1 in the direction opposite to the motion of the cart, the speed of centre of mass of the system is
EASY

In figure E and Vcm represent the total energy and speed of centre of mass of an object of mass 1 kg in pure rolling. The object is:

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MEDIUM

A small ring is rolling without slipping on the circumference of a large bowl as shown below in the figure. The ring is moving down at P1, comes down to the lower most point P2 and is climbing up at P3. Let vCM denote the velocity of the centre of mass of the ring. Choose the correct statement regarding the frictional force on the ring.

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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?
HARD

A plank is moving in a horizontal direction with a constant acceleration ai^. A uniform rough cubical block of side l rests on the plank and is at rest relative to the plank.

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Let the centre of mass of the block be at 0, l2 at a given instant. If a=g10, then the normal reaction exerted by the plank on the block at that instant acts at

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
EASY

If the sum of external forces acting on a system is zero, then the centre of mass

MEDIUM
A square loop of side 2a and carrying current I is kept in xz plane with its centre at origin. A long wire carrying the same current I is placed parallel to z-axis and passing through point 0, b, 0, b>>a. The magnitude of torque on the loop about z-axis will be :
EASY

Two masses A and B, each of mass M are fixed together by a massless spring, A force acts on the mass B as shown in figure. If the mass A starts moving away from mass B with acceleration a, then the acceleration of mass B will be :

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EASY
Two blocks of masses 10 kg and 2 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 12 m s-1 to the heavier block in the direction of the lighter block. Then the velocity of centre of mass is,
MEDIUM
  Define couple. State the SI unit of moment of couple. 
HARD

Four particles A, B, C  and D with masses mA=m,mB=2m,mC=3m  and mD=4m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is:
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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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EASY
The centre of mass of an extended body on the surface of the earth and its centre of gravity
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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EASY

The disc of mass M with uniform surface mass density σ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position xa3π, xa3π where x is _______ . (Round off to the Nearest Integer) [a is an area as shown in the figure]

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MEDIUM

A mass m is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, then with what acceleration will the mass release? (Assume g= acceleration due to gravity)

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MEDIUM
A shell of mass M is fired with a speed u at an angle θ with the horizontal such that it explodes into two equal fragments at the highest point of its trajectory. If one fragment falls vertically, the distance at which the other fragment falls from the point of projection will be,
MEDIUM
In a system of two particles of masses m1 and m2 the second particle is moved by a distance d towards the centre of mass. To keep the centre of mass unchanged, the first particle will have to be moved by a distance
HARD
A rigid uniform bar AB of length L is slipping from its vertical position on a frictionless floor (as shown in the figure). At some instant of time, the angle made by the bar with the vertical is θ. Which of the following statements about its motion is correct?

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