If \(\pi=3.14,\) then the value of \({\pi}^{2}\) is

(a)

9.8596

(b)

9.860

(c)

9.86

(d)

9.9

The dimensional formula of Planck's constant h is

(a)

[ML²T^-1]

(b)

[ML²T³]

(c)

[MLT^-1]

(d)

[ML³T^-3]

The dimensional formula for gravitational constant G is

(a)

[ML³T^-2]

(b)

[M^-1L³T^-2]

(c)

[M^-1L^-3T^-2]

(d)

[ML^-3T²]

Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are taken as three fundamental constants. Which of the following combinations of these has the dimension of length?

(a)

\({{\sqrt{hG}}\over{{c}^{{{3}\over{2}}}}}\)

(b)

\({{\sqrt{hG}}\over{{c}^{{{5}\over{2}}}}}\)

(c)

\(\sqrt{{{hc}\over{G}}}\)

(d)

\(\sqrt{{{Gc}\over{{h}^{{{3}\over{2}}}}}}\)

What is the range of astronomical time scales to microscopic scales?

(a)

10¹⁵S to 10^-15S

(b)

10⁹S to 10^-18S

(c)

10¹⁸S to 10^-22S

(d)

10¹¹S to 10^-16S

Which unit is used to measure size of a nucleus?

(a)

Angstrom

(b)

Micron

(c)

Nano

(d)

Fermi

The dimensions of K.E. is _______________.

(a)

M²L²T^-1

(b)

M¹L¹T¹

(c)

M¹L²T^-2

(d)

M²L²T^-2

Which of the following is true regarding the physical science?

(a)

dealing with non-living things

(b)

dealing with living things

(c)

study with atomic level

(d)

both (a) and (b)

Which relation is wrong?

(a)

1 fermi = 10^-14 m

(b)

r nanometer = 10^-9 m

(c)

1 AU = 1.496 X 10¹¹ m

(d)

1 parsec = 3.26 light year

If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be ______________.

(a)

Ey^-1 T²

(b)

Ey^-2 T²

(c)

Ey¹ T^-2

(d)

Ey^-2 T^-2

Name three practical units to measure Area.

What is meant by Scientific method?

Convert an acceleration of 3 kmh^-2 into an S^-2.

The Moon subtends an angle of 1⁰ 55' at the base line equal to the diameter of the earth. What is the distance of the Moon from the Earth? (Radius of the Earth is 6.4\(\times\)10⁶m)

Round off the following numbers as indicated 248337 up to digits 3 digits

Write the role of physics in technology.

Find the dimensions of a and b in the formula \(\left[ P+{{a\over V^2}} \right][V-b]=RT\) where P is pressure and V is the volume of the gas

State the rules for finding the significant figures in the addition and subtraction of two numbers, with example.

Arrive at Einstein's mass-energy relation by dimensional method (E = mc²).

State the principle of homogeneity. Test the dimensional homogeneity of equations s_n= u+\(\frac { a }{ 2 } \)(2n-1)

Briefly explain the different types of errors and their causes with an example. How can these error be minimised?

A capacitor of capacitance C = 3.0 ± 0.1\(\mu \)F is charged to a voltage of V = 18 ± 0.4 Volt. Calculate the charge Q [Use Q = CV].

The frequency of vibration of a string depends of on,
(i) tension in the string
(ii) mass per unit length of string
(iii) vibrating length of the string
Establish dimensionally the relation for frequency.