  Problem solving tips

## Systems Of Particles And Rotational Motion

- Want to score better marks in exams? Have a look at some problem solving tips.
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Tip 1:
To find the radius of Gyration(K)
i. We consider the mass to be concentrated at a point at a distance x from the centre of mass.
ii. The moment of inertia becomes same for both.
iii. Equate the expression of moment of inertia and find the value of K
Try solving this question:
A
B
C
D
Identify the correct order in which the ratio of radius of gyration to radius increases for the following bodies.
I) rolling solid sphere
II) rolling solid cylinder
III) rolling hollow cylinder
IV) rolling hollow sphere
A
I, II, IV, III
B
I, III, II, IV
C
II, I, IV, III
D
II, I, III, IV
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Tip 2:
DIFFERENT BODIES ROLLING DOWN IN A INCLINED PLANE  Try solving this question:
A solid sphere, a thin-walled hollow sphere, a solid cylinder, a thin-walled hollow cylinder and a ring, each of mass and radius , are simultaneously released at rest from top of an inclined plane, as shown in figure. The objects roll down the plane without slipping. Also we may consider the objects and the surface on which they roll to be perfectly rigid. Match column I and II
List 1Time taken to reach the bottom is maximum forAngular acceleration is maximum forKinetic energy at the bottom is the same forRotational kinetic energy is maximum for
List 2Solid sphereHollow cylinderHollow sphereRing
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Tip 3:
TO FIND ACCELERATION DUE TO PULL:  Try solving this question:
The pulleys in the figure are identical, each having a radius  and moment of inertia Find the acceleration of the block .
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Tip 4:
MAN AND PLANK PROBLEM:  Try solving this question:
A plank of mass and length is at rest on a frictionless floor. The top surface of the plank has friction. At one end of it a man of mass is standing as shown in Fig. If the man walks towards the order end, find the distance, which the plank moves(a) till the man reaches the centre of the plank, (b) till the man reaches the other end of the plank.
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Tip 5
Direction of friction force on rolling object when the force apply at certain height from centre of rotation.  A heavy homogenous cylinder has a mass m and radius R. It is accelerated by a horizontal force F, which is applied through a rope wound around a light drum of radius r attached to the cylinder. The coefficient of static friction is sufficient for the cylinder to roll without slipping :
Choose the correct options :

This question has multiple correct options
A
acceleration of centre of cylinder is
B
friction assumed to be in the opposite direction of F is
C
If a will be greater than
D
Friction assumed to be in the direction of F is