Centre of Mass 4 Question 10
11. A uniform thin of mass and length is standing vertically along the -axis on a smooth horizontal surface, with its lower end at the origin . A slight disturbance at causes the lower end to slip on the smooth surface along the positive -axis, and the rod starts falling. (a) What is the path followed by the centre of mass of the rod during its fall?
(b) Find the equation of the trajectory of a point on the rod located at a distance
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Answer:
Correct Answer: 11. (a) Straight line
(b)
Solution:
- (a) Since, only two forces are acting on the rod, its weight
(vertically downwards) and a normal reaction at point of contact (vertically upwards).
(a)
(b) No horizontal force is acting on the rod (surface is smooth).
Therefore, CM will fall vertically downwards towards negative
(b) Refer figure (b). We have to find the trajectory of a point
Similarly,
or
Squaring and adding Eqs. (i) and (ii), we get
This is an equation of an ellipse. Hence, path of point