Class 11th

This is a short answer type question as classified in NCERT Exemplar

Distance of galaxy = 10²⁵m

Speed of light = 3 $*$ 10⁸ m/s

T = distance /speed = $\frac{{10}^{25}}{3*{10}^8}\approx \frac{1}{3}*{10}^{17}$

$=\frac{10}{3}*{10}^{16}s$

$3.33*{10}^{16}$ s

This is a short answer type question as classified in NCERT Exemplar

(a) A wall clock can measure time correctly upto one second .

(b) A stop watch can measure time correctly upto a fraction of a second .

(c) A digital watch upto the same precision

(d) An atomic clock measure more accurately.

This is a short answer type question as classified in NCERT Exemplar

(a)

 l=R_E; r= 60R_E

$\theta =\frac{R_E}{60R_E}=\frac{1}{60}rad=\frac{1}{60}*\frac{180}{\pi }degree=\frac{3}{\pi }\approx 1^o$

Hence angle subtend is $2^o$

(b) But in 2^nd case it is given that moon is (½)° and earth is 2^o so it become 4 times.

$\frac{diameterofearth}{diameterofmoon}=\frac{2/\pi }{1/2\pi }=4$

(c) To measure parallax sun is about 400 times the earth moon distance hence $\frac{r_{sun}}{r_{moon}}=400$

To finding ratio of

$\frac{D_{sun}}{r_{sun}}=\mathrm{}\frac{D_{sun}}{r_{moon}}$

$\frac{D_{sun}}{D_{moon}}=400$

$\frac{D_{earth}}{D_{moon}}=4$

so $\frac{D_{sun}}{D_{earth}}=100$

so $\frac{D_{sun}}{D_{earth}}=100$

This is a short answer type question as classified in NCERT Exemplarv

Because they cannot be derived from one another as they are independent quantities.

Also we can say that all other quantities in mechanics can be expressed in terms of length mass and time.

This is a short answer type question as classified in NCERT Exemplar

Since f ( $\theta )$ is a sum of different powers of $\theta$  an we know that it is a dimensionless quantity. By principle of homogeneity as RHS is dimensionless. Hence LHS should also be dimensionless.

This is a short answer type question as classified in NCERT Exemplar

One atomic mass unit is 1/12 of the mass of carbon atom

Mass of one carbon atom = 12g

Number of atoms in one mole= Avogadro's number

= 6.023 $*$ 10²³

Mass of one ₆C¹² atom = $\frac{12}{6.023*{10}^{23}}g$

1 amu= 1/12 of mass of carbon atom

1 amu= ( $\frac{1}{12}*\frac{12}{6.023*{10}^{23}}$ )g= 1.67 $*{10}^{-27}kg$

This is a short answer type question as classified in NCERT Exemplar

A mass spectrograph is used for measuring the mass of atoms and molecules.

This is a short answer type question as classified in NCERT Exemplar

Radius of atom = 1A^o=10^-10m

Radius of nucleus = 10^-15m

Volume of atom=V_A= 4/3 $\pi$ r³_a

Volume of nucleus V_N=4/3 $\pi$ r³_N

To finding the ratio

$\frac{V_A}{V_N}=\frac{\frac{4}{3}\pi r_a^3}{\frac{4}{3}\pi r_N^3}=\frac{r_a}{r_n}={10}^{15}$

This is a short answer type question as classified in NCERT Exemplar

The value of any given physical quantity may very over a wide range. Therefore different units of same physical quantity are required. As we know that to measuring distance of an object we need cm m, km, light year etc.