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A rod of length l and radius r is joined...

A rod of length l and radius r is joined to a rod of length `(l)/(2)`and radius `(r)/(2)`of same material. The free end of small rod is fixed to a rigid base and the free end of larger rod is given a twist of `theta^(@)`, the twist angle at the joint will be

Text Solution

Verified by Experts

`theta_1 + theta_2 = theta to (1) ` we know that `theta prop (l)/(r^4)`
` therefore theta_1/theta_2 = l_1/l_2 xx(r_2^4)/(r_1^4) = (l//2)/(l) xx (r^4)/((r//2)^4) = 8`

` theta_1/theta_2 = 8 to (2)`
After solving equation (1)and (2) , we get
` thete_1 = 8/9 theta `
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