Com of Solid Bodies
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- False
- True
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- True
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- (3, 4) m
- (4, 3) m
- (3, 3) m
- (4, 4) m
lf all the particles of a system lie in a cube, is it necessary that the centre of mass be in the cube?
Yes
No
Sometimes
Maybe
Figure shows a uniform disc of radius R, from which a hole of radius R2 has been cut out from left of the center and is placed on right of the center of disc. Find the centre of mass of the resulting disc.
(R4, 0)
(−R4, 0)
(R6, 0)
(−R6, 0)
A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surfaced of a fixed table. Initially the right edge of the block is at x = 0, in a coordinate system fixed to the table. A point mass m is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block, its position is x and the velocity is v. At that instant, which of the following option is/are correct ?
The velocity of the point mass m is v=√2gR1+mM.
The x component of displacement of the centre of mass of the block M is −mRM+m.
The position of the point mass is x= −√2mRM+m.
The velocity of the block M is V= −mM√2gR.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1017793/original_original_02_S1.png)
- (0, 0)
- ⎛⎜ ⎜⎝2Rsinα2α, 0⎞⎟ ⎟⎠
- ⎛⎜ ⎜⎝2Rcosα2α, 2Rcosα2α⎞⎟ ⎟⎠
- ⎛⎜ ⎜⎝0, 2Rsinα2α⎞⎟ ⎟⎠
Half of the rectangular plate shown in figure is made of a material of density p1 and the other half of density p2. The length of the plate is L. Locate the centre of mass of the plate.
[p1+4p23(p1+p2)]2
[2p1+3p25(p1+p2)]2
[p1+3p24(p1+p2)]2
[2p1+5p23(p1+2p2)]2