A hypothetical experiment conducted to determine Youngs formula Y=( cos θ Tx.τ /l3) . If Y = Youngs modulus, T = time period, t = Torque and l= length, then find the value of x .

Question

A hypothetical experiment conducted to determine Youngs formula Y=( cos θ Tx.τ /l3) . If Y = Youngs modulus, T = time period, t = Torque and l= length, then find the value of x . (A) zero (B) 1 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

y=( cos θ Tx.τ /l3) [y]=[ML-1T-2][T]=[T2] [T]=[ML2T-2] θ = dimensionless (l)=[L] [ML-1T-2]=([T]x[ML2T-2]/[L3]) comparing the power, -2+x=-2 x=0

Q. A hypothetical experiment conducted to determine Youngs formula $Y = \frac{c o s θ T ^{x} . τ}{l ^{3}}$ .
If Y = Youngs modulus, T = time period,
t = Torque and $l =$ length, then find the value of $x$ .

zero

1

2

3

$y = \frac{c o s θ T ^{x} . τ}{l ^{3}}$
$[y] = [M L^{- 1} T^{- 2}] [T] = [T^{2}]$
$[T] = [M L^{2} T^{- 2}]$
$θ =$ dimensionless $(l) = [L]$
$[M L^{- 1} T^{- 2}] = \frac{[ T ] ^{x} [ M L ^{2} T ^{- 2} ]}{[ L ^{3} ]}$
comparing the power,
$- 2 + x = - 2$ $x = 0$

Q. A hypothetical experiment conducted to determine Youngs formula Y=l3cosθTx.τ​ . If Y = Youngs modulus, T = time period, t = Torque and l= length, then find the value of x .

zero

1

2

3

y=l3cosθTx.τ​ [y]=[ML−1T−2][T]=[T2] [T]=[ML2T−2] θ= dimensionless (l)=[L] [ML−1T−2]=[L3][T]x[ML2T−2]​ comparing the power, −2+x=−2 x=0

Q. A hypothetical experiment conducted to determine Youngs formula $Y = \frac{c o s θ T ^{x} . τ}{l ^{3}}$ .
If Y = Youngs modulus, T = time period,
t = Torque and $l =$ length, then find the value of $x$ .

$y = \frac{c o s θ T ^{x} . τ}{l ^{3}}$
$[y] = [M L^{- 1} T^{- 2}] [T] = [T^{2}]$
$[T] = [M L^{2} T^{- 2}]$
$θ =$ dimensionless $(l) = [L]$
$[M L^{- 1} T^{- 2}] = \frac{[ T ] ^{x} [ M L ^{2} T ^{- 2} ]}{[ L ^{3} ]}$
comparing the power,
$- 2 + x = - 2$ $x = 0$