**Question 49 (Textile Technology & Fibre Science)**

The diameter and length of torsion rod used in a projectile loom are increased by 5% and 20%, respectively. If the torque required to twist the rod increases by X%, then the value of X, accurate to two decimal places, is __**1.27 to 1.31**__.

**[Show Answer]**

Write Here

**Given**–

Let ,**initial** **diameter** of **torsional rod=d _{1}**

Then,

**final**

**diameter**of

**torsional rod**(

**d**)=d

_{2}_{1}+d

_{1}x

**5%**

d

_{2}=d

_{1}+(d

_{1}x 5/100)

d

_{2}=d

_{1}+d

_{1}x 0.05

**d**

_{2}=1.05 x d_{1}Let,

**initial length of torsional rod**=

**l**

_{1}Then,

**final length of torsional rod**(

**l**)=l

_{2}_{1}+l

_{1}x 20%

l

_{2}=l

_{1}+(l

_{1}x 20/100)

l

_{2}=l

_{1}+0.20 x l

_{1}

**l**

_{2}=1.2 xl_{1}Let,

**initial**

**torque**required to twist the rod=

Then,

**final torque**required to twist the rod

**By formula**:

Where, is

**torque**,

**d**is

**diameter**of rod and

**l**is

**length**of torsional rod

So,

(

**Answer)**