A hypothetical experiment conducted to determine Young's formula Y=( cos θ Tx ⋅ τ/l3) . If Y= Young's modulus, T= time period, τ= torque and l= length, then find the value of x

Question

A hypothetical experiment conducted to determine Young's formula Y=( cos θ Tx ⋅ τ/l3) . If Y= Young's modulus, T= time period, τ= torque and l= length, then find the value of x (A) zero (B) 1 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

We have, Y=( cos θ Tx ⋅ τ/l3) ...(i) We know, [Y]=[M L-1 T-2],[T]=[T1] [τ]=[M L2 T-2] θ= dimensionless [l]=[L] Thus, Eq. (i) becomes [M L-1 T-2]=([T1]x [M L2 T-2]/[L3]) or [M L-1 T-2]=[M L-1 T-2+x] Comparing the powers, we have -2+x=-2 ∴ x=0

Q. A hypothetical experiment conducted to determine Young's formula Y=l3cosθTx⋅τ​. If Y= Young's modulus, T= time period, τ= torque and l= length, then find the value of x

zero

1

2

3

We have, Y=l3cosθTx⋅τ​ ...(i) We know, [Y]=[ML−1T−2],[T]=[T1] [τ]=[ML2T−2] θ= dimensionless [l]=[L] Thus, Eq. (i) becomes [ML−1T−2]=[L3][T1]x[ML2T−2]​ or [ML−1T−2]=[ML−1T−2+x] Comparing the powers, we have −2+x=−2 ∴x=0

Q. A hypothetical experiment conducted to determine Young's formula $Y = \frac{c o s θ T ^{x} \cdot τ}{l ^{3}} .$ If
$Y =$ Young's modulus,
$T =$ time period,
$τ =$ torque and
$l =$ length, then find the value of $x$