FRAC{{\pi {d^4}}}{{32}} = \frac{\pi }{{32}}\left[ {d_0^4 - d_i^4} \RIGHT]\)\(\Rightarrow {d_o} > d \Rightarrow {r_0} > r\)Now, angle of TWIST\(\theta = \frac{{TL}}{{GJ}}\)∴ θS = θH ----(1) (∵ T, L, G, J all are same for solid and Hollow shaft)\(\tau = \frac{{TR}}{J}\)\(\Rightarrow {\tau _{max}}\;for\;solid\;shaft = \frac{T}{J}.r\)\({\tau _{max}}\;for\;hollow\;shaft = \frac{T}{J}.{r_0}\)∵ r0 > r∴ (τmax)H > (τmax)S ----(2)Hence from (1) and (2) we can see that the correct option is d.

"> FRAC{{\pi {d^4}}}{{32}} = \frac{\pi }{{32}}\left[ {d_0^4 - d_i^4} \RIGHT]\)\(\Rightarrow {d_o} > d \Rightarrow {r_0} > r\)Now, angle of TWIST\(\theta = \frac{{TL}}{{GJ}}\)∴ θS = θH ----(1) (∵ T, L, G, J all are same for solid and Hollow shaft)\(\tau = \frac{{TR}}{J}\)\(\Rightarrow {\tau _{max}}\;for\;solid\;shaft = \frac{T}{J}.r\)\({\tau _{max}}\;for\;hollow\;shaft = \frac{T}{J}.{r_0}\)∵ r0 > r∴ (τmax)H > (τmax)S ----(2)Hence from (1) and (2) we can see that the correct option is d.

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Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, θs is the twist and τs is the maximum shear stress in the solid shaft, whereas θH is the twist and τH is the maximum shear stress in the hollow shaft. Which one of the following is TRUE?

Current Affairs General Awareness in Current Affairs 9 months ago

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Given:-LS = LH, TS = TH = T, JS = JH (Where L = length, T = torque, J = Polar moment of inertia)∵ JS = JH\(\FRAC{{\pi {d^4}}}{{32}} = \frac{\pi }{{32}}\left[ {d_0^4 - d_i^4} \RIGHT]\)\(\Rightarrow {d_o} > d \Rightarrow {r_0} > r\)Now, angle of TWIST\(\theta = \frac{{TL}}{{GJ}}\)∴ θS = θH ----(1) (∵ T, L, G, J all are same for solid and Hollow shaft)\(\tau = \frac{{TR}}{J}\)\(\Rightarrow {\tau _{max}}\;for\;solid\;shaft = \frac{T}{J}.r\)\({\tau _{max}}\;for\;hollow\;shaft = \frac{T}{J}.{r_0}\)∵ r0 > r∴ (τmax)H > (τmax)S ----(2)Hence from (1) and (2) we can see that the correct option is d.

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Posted on 01 Nov 2024, this text provides information on Current Affairs related to General Awareness in Current Affairs. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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