The temperatures of two bodies measured by a thermometer are \(t_1=20^\circ \text{C}\pm0.5^\circ \text{C}\) and \(t_2=50^\circ \text{C}\pm0.5^\circ \text{C}.\) The temperature difference with permissible error is:
1. \(31^\circ \text{C}\pm0.5^\circ \text{C}\)
2. \(30^\circ \text{C}\pm1.0^\circ \text{C}\)
3. \(30^\circ \text{C}\pm0.0^\circ \text{C}\)
4. \(30^\circ \text{C}\pm1.5^\circ \text{C}\)

The resistance \(R=\frac{V}{I}\) where \(V=(100 \pm 5) ~V\) and \(I=(10 \pm 0.2)~ A\). The percentage error in \(R\) is:
1. \(5\%\)
2. \(2\%\)
3. \(7\%\)
4. \(3\%\)

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

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

The relative error in \(Z,\) if \(Z=\frac{A^{4}B^{1/3}}{CD^{3/2}}\) is:
1. \(\frac{\Delta A}{A}+\frac{\Delta B}{B}+\frac{\Delta C}{C}+\frac{\Delta D}{D}\)

2. \(4\frac{\Delta A}{A}+\frac{1}{3}\frac{\Delta B}{B}-\frac{\Delta C}{C}- \frac{3}{2}\frac{\Delta D}{D}\)

3. \(4\frac{\Delta A}{A}+\frac{1}{3}\frac{\Delta B}{B}+\frac{\Delta C}{C}+\frac{2}{3}\frac{\Delta D}{D}\)

4. \(4\frac{\Delta A}{A}+\frac{1}{3}\frac{\Delta B}{B}+\frac{\Delta C}{C}+\frac{3}{2}\frac{\Delta D}{D}\)

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 \(7.203\) \(\mathrm{m}.\) What are the total surface area and the volume respectively of the cube to appropriate significant figures?

5.74 g of a substance occupies \(1.2~\mathrm{cm^3}\). Its density by keeping the significant figures in view is:
1. \(4.7333~\mathrm{g/cm^3}\)
2. \(3.8~\mathrm{g/cm^3}\)
3. \(4.8~\mathrm{g/cm^3}\)
4. \(3.7833~\mathrm{g/cm^3}\)

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 \(\frac{1}{2}mv^2=mgh\) 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: