If there is an error of 1% in the calculation | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The moment of inertia of a disc about an axis tangent to it is given by the parallel axis theorem: $I = I_{cm} + MR^2 = \frac{1}{2}MR^2 + MR^2 = \

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) The moment of inertia of a disc about an axis tangent to it is given by the parallel axis theorem: $I = I_{cm} + MR^2 = \frac{1}{2}MR^2 + MR^2 = \frac{3}{2}MR^2$.However,for a disc,the moment of inertia about a tangent in its plane is $I = \frac{5}{4}MR^2$.Using the relative error formula for $I = k M^a R^b$,we have $\frac{\Delta I}{I} = a \frac{\Delta M}{M} + b \frac{\Delta R}{R}$.Here,$a = 1$ and $b = 2$.Given $\frac{\Delta M}{M} = 1\%$ and $\frac{\Delta R}{R} = 1.5\%$.Therefore,$\frac{\Delta I}{I} 	imes 100 = (1 	imes 1\%) + (2 	imes 1.5\%) = 1\% + 3\% = 4\%$.

If there is an error of $1\%$ in the calculation of the mass of a disc and $1.5\%$ error in the radius,then the $\%$ error in the moment of inertia about an axis tangent to the disc is .......... $\%$

Similar Questions

$A$ cylindrical wire has a mass $(0.3 \pm 0.003) \text{ g}$,radius $(0.5 \pm 0.005) \text{ mm}$ and length $(6 \pm 0.06) \text{ cm}$. The maximum percentage error in the measurement of its density is (in $\%$)

The two specific heat capacities of a gas are measured as $C_P = (12.28 \pm 0.2) \text{ units}$ and $C_V = (3.97 \pm 0.3) \text{ units}$. Find the value of the gas constant $(R)$.

Out of absolute error,relative error,and fractional error,which has a unit and which has no unit?

$A$ set of defective observation weights is used by a student to find the mass of an object using a physical balance. $A$ large number of readings will reduce:

Vedclass Test Series

Exam Paper Generator

Online Exam Module