Newtons Laws Of Motion

In the right angle

%5CDelta

PQR

%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20t%5E2%3Dc%5E2%2By%5E2

Differentiating this
equation with respect to
time, we ge

2t%5Cfrac%7Bdl%7D%7Bdt%7D%3D0%2B2y%5Cfrac%7Bdy%7D%7Bdt%7D

%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5Cbig(-%5Cfrac%7Bdy%7D%7Bdt%7D%5Cbigg)%3D%5Cfrac%7Bl%7D%7By%7D%5Cbigg(-%5Cfrac%7Bdl%7D%7Bdt%7D%5Cbigg)

Here%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20-%5Cfrac%7Bdy%7D%7Bdt%7D%3Dv_%7BM%7D%20%5C%2C%20%5C%2C%20%5C%2C%20%5CRightarrow%20%5C%2C%20%5C%2C%20%5C%2C%20%5Cfrac%7B1%7D%7By%7D%3D%5Cfrac%7B1%7D%7Bcos%5Ctheta%7D

and -dl / dt =U
Hence,

%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20v_M%3D%5Cfrac%7BU%7D%7Bcos%5Ctheta%7D

%5Ctherefore%20%5C%2C%20%5C%2C

Correct option is (b).
Hence ,

%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20v_M%3D%5Cfrac%7BU%7D%7Bcos%5Ctheta%7D

%5Ctherefore%20%5C%2C%20%5C%2C

Correct option is (b).

If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation

z%20%3D%20x%2Fy

. If the errors in

x%20%2Cy

and

z

are

%5CDelta%20x%2C%20%5CDelta%20y

and

%5CDelta%20z

, respectively, then

z%20%5Cpm%20%5CDelta%20z%20%3D%20%5Cfrac%7Bx%20%5Cpm%20%5CDelta%20x%7D%7By%20%5Cpm%20%5CDelta%20y%7D%20%3D%20%5Cfrac%7Bx%7D%7By%7D%20%5Cleft(%201%20%5Cpm%20%5Cfrac%7B%5CDelta%20x%7D%7Bx%7D%20%5Cright)%20%5Cleft(%201%20%5Cpm%20%5Cfrac%7B%5CDelta%20y%7D%7By%7D%20%5Cright)%5E%7B-1%7D

. The series expansion for

%5Cleft(%201%20%5Cpm%20%5Cfrac%7B%5CDelta%20y%7D%7By%7D%20%5Cright)%5E%7B-1%7D

, to first power in

%5CDelta%20y%2Fy

. is

1%20%5Cmp%20(%5CDelta%20y%20%2F%20y%20)

. The relative errors in independent variables are always added. So the error in

z

will be

%5CDelta%20z%20%3D%20z%20%5Cleft(%20%5Cfrac%7B%5CDelta%20x%7D%7Bx%7D%20%2B%20%5Cfrac%7B%5CDelta%20y%7D%7By%7D%20%5Cright)

. The above derivation makes the assumption that $\Delta powers of these quantities are neglected. Consider the ratio

r%20%3D%20%5Cfrac%7B(1-a)%7D%7B(1%2Ba)%7D

to be determined by measuring a dimensionless quantity

a

. If the error in the measurement of

a

%5CDelta%20a%20(%5CDelta%20a%2Fa%20%3F%3F1)

, then what is the error

%5CDelta%20r

in determining

r

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

Newtons Laws Of Motion

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

Chapter Questions
2 MCQs