Question

A uniform rectangular plate is heated from 0°c to 100°c . Initial area of plate is 10cm^2. the linear coefficient of the material of the plate is 18×10^-6k . What is the shift of the center of mass

Answer 1

shift of centre of mass of rectangular plate is zero

first find change in length and its breadth.

let initial length of rectangular plate is l and breadth is b.

so, change in length, ∆l = lα∆T

= l × 18 × 10^-6 × 100

= 0.0018l

percentage increase in length = ∆l/l × 100 = 0.0018 × 100 = 0.18%

similarly, change in breadth, ∆b = bα∆T

= b × 18 × 10^-6 × 100

= 0.0018b

percentage increase in breadth = 0.0018 × 100 = 0.18%

we see, percentage change in length and breadth is same. so, expansion of length and breadth will be symmetrical and hence, position centre of mass of rectangular plate remains constant.

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Answer 2

$\huge\bold\purple{Answer:-}$

first find change in length and its breadth.

let initial length of rectangular plate is l and breadth is b.

so, change in length, ∆l = lα∆T

= l × 18 × 10^-6 × 100

= 0.0018l

percentage increase in length = ∆l/l × 100 = 0.0018 × 100 = 0.18%

similarly, change in breadth, ∆b = bα∆T

= b × 18 × 10^-6 × 100

= 0.0018b

percentage increase in breadth = 0.0018 × 100 = 0.18%

we see, percentage change in length and breadth is same. so, expansion of length and breadth will be symmetrical and hence, position centre of mass of rectangular plate remains constant.