The angle of $1°$ (degree) will be equal to:

(Use $360°=2\mathrm{\pi } \mathrm{rad}, 1°=60\text{'} \mathrm{and} 1\text{'}=60\text{'}\text{'}$)

$$\begin{gathered} \left(1\right) 1.034\times {10}^{-3} \mathrm{rad} \\ \left(2\right) 1.745\times {10}^{-2} \mathrm{rad} \\ \left(3\right)1.524\times {10}^{-2} \mathrm{rad} \\ \left(4\right) 1.745\times {10}^{+3} \mathrm{rad} \end{gathered}$$

A man wishes to estimate the distance of a nearby tower from him. He stands at point A in front of tower C and spots a very distant object O in line with AC. He then walks perpendicular to AC up to B, a distance of 100 m, and looks at O and C again. Since O is very distant, the direction BO is practically the same as AO; but he finds the line of sight of C shifted from the original line of sight by an angle θ = $40°$ (θ is known as ‘parallax’), the distance of the tower C from his original position A is:

The moon is observed from two diametrically opposite points A and B on Earth. The angle θ subtended at the moon by the two directions of observation is $1°$ 54′. Given the diameter of the Earth to be about 1.276 × ${10}^7$ m, the distance of the moon from the Earth is:

$$\begin{gathered} \left(1\right) 2.91\times {10}^8 \mathrm{m} \\ \left(2\right) 3.11\times {10}^9 \mathrm{m} \\ \left(3\right) 3.84\times {10}^8 \mathrm{m} \\ \left(4\right) 1.91\times {10}^7 \mathrm{m} \end{gathered}$$

The Sun’s angular diameter is measured to be 1920′′. The distance D of the Sun from the Earth is $1.496\times {10}^{11} \mathrm{m}.$ The diameter of the Sun:

If the size of a nucleus (in the range of ${10}^{-15} \mathrm{to} {10}^{-14} \mathrm{m}$) is scaled up to the tip of a sharp pin, what roughly is the size of an atom? Assume tip of the pin to be in the range ${10}^{-5} \mathrm{m} \mathrm{to} {10}^{-4} \mathrm{m}.$

Two clocks are being tested against a standard clock located in a national laboratory. At 12:00:00 noon by the standard clock, the readings of the two clocks are :

                                               Clock 1                             Clock 2

Monday                                  12:00:05                           10:15:06

Tuesday                                  12:01:15                           10:14:59

Wednesday                             11:59:08                           10:15:18

Thursday                                12:01:50                           10:15:07

Friday                                     11:59:15                           10:14:53

Saturday                                 12:01:30                           10:15:24

Sunday                                   12:01:19                           10:15:11

If you are doing an experiment that requires precision time interval measurements, which of the two clocks will you prefer?

We measure the period of oscillation of a simple pendulum. In successive measurements, the readings turn out to be 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s. The average absolute error and percentage error, respectively, are:

The temperatures of two bodies measured by a thermometer are

${\mathrm{t}}_1$ = 20 ^oC ± 0.5 ^oC and ${\mathrm{t}}_2$ = 50 ^oC ± 0.5 ^oC.

The temperature difference with permissible error is:

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:

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:

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

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:

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:

If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.

If E and G respectively denote energy and gravitational constant, then $\frac{\mathrm{E}}{\mathrm{G}}$ has the dimensions of:

The number of significant digits in 1001, 100.1, 100.10, 0.001001 are, respectively,: