Question

A uniform rod of mass M and length L is rotated in horizontal plane about a vertical axis with angular velocity omega as shown in the figure. The tension in the rod at Point P is
1 or 2

1) Mw²(L²-x²) / L
2) Mw²(L²-x²)/ 2L​

Answer 1

Answer:

The mass of the element =dm=

l

m

dx

The force on the element towards the axis =T−(T+dT)=−dT

∴−dT=(dm)ω

2

x=(

l

m

dx)ω

2

x

T=−

l

mω

2

.

2

x

2

+constant

For x=1,T=0. ∴the constant=

2

1

.

l

mω

2

l

2

∴T=

2

1

.

l

mω

2

(l

2

−x

2

)