The relative error in Z, if Z = $\frac{{\mathrm{A}}^4{\mathrm{B}}^{1/3}}{{\mathrm{CD}}^{3/2}}$ is: 

1.  $\frac{∆A}{A}+\frac{∆B}{B }+\frac{∆C}{C}+\frac{∆D}{D}$

2.  $4\frac{∆A}{A}+\frac{1}{3}\frac{∆B}{B }-\frac{∆C}{C}-\frac{3}{2}\frac{∆D}{D}$

3.  $4\frac{∆A}{A}+\frac{1}{3}\frac{∆B}{B }+\frac{∆C}{C}+\frac{2}{3}\frac{∆D}{D}$

4.  $4\frac{∆A}{A}+\frac{1}{3}\frac{∆B}{B }+\frac{∆C}{C}+\frac{3}{2}\frac{∆D}{D}$

The period of oscillation of a simple pendulum is $\mathrm{T} =2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{g}}}$. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. The percentage error in g is:

1.  $2\%$

2.  $3\%$

3.  $5\%$

4.  $0\%$

Each side of a cube is measured to be 7.203 m. What are the total surface area and the volume respectively of the cube to appropriate significant figures?

1.  $373.7 {\mathrm{m}}^3 \mathrm{and} 311.3 {\mathrm{m}}^2$

2. $311.3 {\mathrm{m}}^2 \mathrm{and} 373.7 {\mathrm{m}}^3$ 

3.  $311.2992 {\mathrm{m}}^2 \mathrm{and} 373.7147 {\mathrm{m}}^3$

4.  $373.7147 {\mathrm{m}}^3 \mathrm{and} 311.2992 {\mathrm{m}}^2$

5.74 g of a substance occupies 1.2 ${\mathrm{cm}}^3$. Its density by keeping the significant figures in view is:

1.  4.7333 $\mathrm{g}/{\mathrm{cm}}^3$

2.  3.8 $\mathrm{g}/{\mathrm{cm}}^3$

3.  4.8 $\mathrm{g}/{\mathrm{cm}}^3$

4.  3.7833 $\mathrm{g}/{\mathrm{cm}}^3$

The SI unit of energy is $\mathrm{J} = {\mathrm{kgm}}^2{\mathrm{s}}^{-2}$; that of speed v is ${\mathrm{ms}}^{-1}$ and of acceleration a is ${\mathrm{ms}}^{-2}$. Which of the formula for kinetic energy (K) given below can you rule out on the basis of dimensional arguments (m stands for the mass of the body)?

(a) K = ${\mathrm{m}}^2{\mathrm{v}}^3$

(b) K = $\left(1/2\right){\mathrm{mv}}^2$

(c) K = ma

(d) K = (3/16)${\mathrm{mv}}^2$

(e) K = (1/2)${\mathrm{mv}}^2$+ma

1.  (a), (c) & (d)

2.  (b) & (d)

3.  (a), (c), (d) & (e)

4.  (a), (c) & (e)

Let us consider an equation $\frac{1}{2}{\mathrm{mv}}^2=\mathrm{mgh}$ where m is the mass of the body, v its velocity, g is the acceleration due to gravity and h is the height. The equation is:

(1) dimensionally correct.

(2) dimensionally incorrect.

(3) can not be checked by dimensional analysis.

(4) can't say anything.

Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length (l), the mass of the bob (m) and acceleration due to gravity (g). Expression for its time period is:

1.  $\mathrm{T} = \frac{1}{2\mathrm{\pi }}\sqrt{\frac{\mathrm{l}}{\mathrm{g}}}$

2.  $\mathrm{T} = 2\mathrm{\pi }\left(\frac{\mathrm{l}}{\mathrm{g}}\right)$

3.  $\mathrm{T} = 2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\mathrm{g}}}$

4.  $\mathrm{T} = 2\mathrm{\pi }\sqrt{\frac{\mathrm{g}}{\mathrm{l}}}$

Two resistors of resistances ${\mathrm{R}}_1 = \left(100 \pm 3\right)$ ohm and ${\mathrm{R}}_2 = \left(200 \pm 4\right)$ ohm are connected in parallel. The equivalent resistance of the parallel combination is:

1.  (300 ± 7) ohm

2.  (66.7 ± 7) ohm

3.  (66.7 ± 1.8) ohm

4.  (100 ± 1) ohm

Two resistors of resistances ${\mathrm{R}}_1 = \left(100 \pm 3\right)$ ohm and $R_2 = \left(200 \pm 4\right)$ ohm are connected in series, the equivalent resistance of the series combination is:

1.  (300 ± 7) ohm

2.  (300 ± 1) ohm

3.  (300 ± 0) ohm

4.  (100 ± 1) ohm

The resistance R = $\frac{\mathrm{V}}{\mathrm{I}}$ where V = (100 ± 5)V and I = (10 ± 0.2)A. The percentage error in R is:

1.  $5\%$

2.  $2\%$

3.  $7\%$

4.  $3\%$