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A rod of length 50cm is pivoted at one end. It is raised such that it makes an angle of 30 degrees from the horizontal and is then released from rest. Its angular speed when it passes through the horizontal (in rad/sec) will be (g=10 ms -2 ) √15 √30 √10 √30 /2 Plz explain....

A rod of length 50cm is pivoted at one end. It is raised such that it makes an angle of 30 degrees from the horizontal and is then released from rest. Its angular speed when it passes through the horizontal (in rad/sec) will be (g=10 ms-2)
  1. √15
  2. √30
  3. √10
  4. √30 /2
Plz explain....

Grade:12th pass

2 Answers

Arun
25750 Points
3 years ago
Work done by gravity from initial to final
position is,
 
W=mg 
2
ℓ
​ 
 sin30 
o
 
 
= 
4
mgℓ
​ 
 
 
According to work-energy theorem
 
W= 
2
1
​ 
 Iω 
2
 
 
⇒ 
2
1
​ 
  
3
mℓ 
2
 
​ 
 ω 
2
 = 
4
mgℓ
​ 
 
 
ω= 
2ℓ
3g
​ 
 
​ 
 = 
2×0.5
3×10
​ 
 
​ 
 
 
ω= 
30
​ 
  rad/sec
Vikas TU
14149 Points
3 years ago
Dear student 
A rod of length 50cm is provided at one end. It is raised such that if makes an angle of 30^{\circ} from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal ( in rad s-1) will be (g = 10ms-2)
Explanation:
By work energy theorum,
mgl/4=1/2×Iw²
mgl/4 =ml²w²/3×2
w²=√3g/2l=√30

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