System Of Particles

Question 1

COM for uniform rod

Answer 1

L/2

Question 2

COM for semicircular ring

Answer 2

2R/π

Question 3

COM for semicircular disc

Answer 3

4R/3 π

Question 4

COM for solid hemisphere

Answer 4

3R/8

Question 5

COM for hollow hemisphere

Answer 5

R/2

Question 6

COM of triangle

Answer 6

H/ 3

Question 7

COM of cone, triangular or square pyramid

Answer 7

H/4

Question 8

For oblique collision (elasticaly)-identical spheres with one of them at rest.

1) velocities of the bodies are perpendicular.
2) resultant of final velocities is the initial velocity.

a) both are correct.
b) both are wrong.
c) only 1) is correct.
d) only 2) is correct.
e) can’t say anything.

Answer 8

Both are correct.

Question 9

MI for uniform rod with axis passing through centre and perpendicular to rod

Answer 9

ML²/12

Question 10

MI for Uniform rod with axis passing through end points perpendicular to the rod

Answer 10

ML²/3

Question 11

MI for Uniform rod with axis at an angle theta with vertical

Answer 11

ML² sin² θ /3

Question 12

MI for uniform ring with axis passing through centre perpendicular to the plane of ring

Answer 12

MR²

Question 13

MI of uniform disc with axis passing through perpendicular the plane of disc.

Answer 13

MR² /2

Question 14

MI of uniform hollow sphere M,R with diametric axis

Answer 14

2MR² /3

Question 15

MI for solid sphere M,R with diametric axis

Answer 15

2MR² /5

Question 16

MI for hollow cylinder M,R with axis as it’s own axis

Answer 16

MR²

Question 17

Parallel axis theorem states that

Answer 17

I// = Icm + Md²
## axis passing through the center of mass

Question 18

Perpendicular axis theorem states that

Answer 18

Iz = Iy + Ix 
## only applicable for laminar/planar bodies.