The length of a cylinder is measured with a meter rod having the least count of \(0.1~\text{cm}\). Its diameter is measured with vernier callipers having the least count of \(0.01~\text{cm}\). Given that the length is \(5.0~\text{cm}\) and the radius is \(2.0~\text{cm}\). The percentage error in the calculated value of the volume will be:

1.	\(1\%\)	2.	\(2\%\)
3.	\(3\%\)	4.	\(4\%\)

In an experiment, the following observations were recorded: initial length \(L =2.820~\text{m}\), mass \(M = 3.00~\text{kg}\), change in length \(l = 0.087~\text{cm}\), diameter \(D = 0.041~\text{cm}\). Taking \(g = 9.81~\text{m/s}^2\) and using the formula, \(Y = \dfrac{4MgL}{\pi D^2l},\) the maximum permissible error in \(Y \) will be:
1. \(7.96\%\)
2. \(4.56\%\)
3. \(6.50\%\)
4. \(8.42\%\)

According to Joule's law of heating, heat produced H = I²Rt, where I is current, R is resistance and t is time. If the errors in the measurement of I, R and t are 3%, 4% and 6% respectively then error in the measurement of H is

(1) ± 17%

(2) ± 16%

(3) ± 19%

(4) ± 25%

If there is a positive error of \(50\%\) in the measurement of the velocity of a body, then the error in the measurement of kinetic energy is:
1. \(25\%\)
2. \(50\%\)
3. \(100\%\)
4. \(125\%\)

A physical quantity \(P\) is given by \(P=\dfrac{A^3 B^{1/2}}{C^{-4}D^{3/2}}.\) The quantity which contributes the maximum percentage error in \(P\) is:

If L = 2.331 cm, B = 2.1 cm, then L + B =?

1. 4.431 cm

2. 4.43 cm

3. 4.4 cm

4. 4 cm

If the length of rod A is 3.25 ± 0.01 cm and that of B is 4.19 ± 0.01 cm then the rod B is longer than rod A by 

(1) 0.94 ± 0.00 cm

(2) 0.94 ± 0.01 cm

(3) 0.94 ± 0.02 cm

(4) 0.94 ± 0.005 cm

A physical quantity is given by $X=M^a{L}^b{T}^c$. The percentage error in measurement of M, L and T are $\alpha ,\beta$ and $\gamma$ respectively. Then maximum percentage error in the quantity X is

1. $a\alpha +b\beta +c\gamma$

2. $a\alpha +b\beta -c\gamma$

3. $\frac{a}{\alpha }+\frac{b}{\beta }+\frac{c}{\gamma }$

4. None of these

A physical quantity \(A\) is related to four observable quantities \(a\), \(b\), \(c\) and \(d\) as follows, \(A= \frac{a^2b^3}{c\sqrt{d}},\) the percentage errors of measurement in \(a\), \(b\), \(c\) and \(d\) are \(1\%\), \(3\%\), \(2\%\) and \(2\%\) respectively. The percentage error in quantity \(A\) will be: 
1. \(12\%\)
2. \(7\%\)
3. \(5\%\)
4. \(14\%\)

If the acceleration due to gravity is 10 ms^–2 and the units of length and time are changed in kilometer and hour respectively, the numerical value of the acceleration is 

(1) 360000

(2) 72,000

(3) 36,000

(4) 129600