A circular rod which tapers uniformly from 30 mm diameter to 20 mm diameter and another rectangular bar of constant thickness 5 mm and uniformly tapering in width from 20 mm to 10 mm. The length and applied axial load are same for both the bars, the ratio of the elongation in the respective bar is ? (Take $E = 2 \times 10^{5} N / m m^{2}$ for both material)

0.25

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0.15

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

0.50

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6.67

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $0.15$
Extension of uniformly tapering circular rod due to axial load=

$= \frac{4 P L}{π E D_{1} D_{2}}$

$= \frac{4 \times P \times L}{π \times 2 \times 10^{5} \times 30 \times 20}$

Extension of uniformly tapering rectangular bar

$= \frac{P L}{E t (B_{1} - B_{2})} l o g_{e} (\frac{B_{1}}{B_{2}})$

$= \frac{P L}{2 \times 10^{5} \times 5 (20 - 10)} \times l o g_{e} (\frac{20}{10})$

$Required ratio = \frac{\frac{4 P L}{π E \times 30 \times 20}}{\frac{P L}{E t (20 - 10) l o g_{e} (2)}}$

$= \frac{4}{π \times 30 \times 20} \times \frac{5 \times 10}{l o g_{e} (2)} = 0.153$

Suggest Corrections

Similar questions

Q. A mild steel bar of length

450 m m

tapers uniformly. The diameters at the ends are

36 m m

and

18 m m

, respectively. An axial load of

12 k N

is applied on the bar.

E = 2 \times 10^{5} N / m m^{2}

. The elongation of the bar will be

Q. A tapered circualr rod of diameter varying from

30 m m

15 m m

is connected to another circular rod of diameter

15 m m

as shown in figure. Both bars are of same material with the modulus of elasticity

E = 2 \times 10^{5} N / m m^{2}

and subjected to axial load of

100 k N

, then deflection of a bar at the free end is ____

m m

A tapered circular rod of diameter varying from 60 mm tp 40 mm is connected to another circular tapered rod of diameter varying from 40 mm to 70 mm as shown in the figure below. Both bars are of the same material with $E = 2 \times 10^{5} MPa$ . When subjected to a load of 100 kN, the deflection at point A is mm.