Ncert Exercises & Solutions

Choose the incorrect statement from the given ones:

1.	$1~\mathrm{kgm^2s^{-2}}=10^{7}~\mathrm{gcm^2s^{-2}}$
2.	$1~\text m=1.057\times10^{-16}~\text{ly}$
3.	$3.0~\mathrm{m/s^2}=10.8~\mathrm{km/h}$
4.	$G=6.67\times10^{-11}~\mathrm{Nm^2/kg^2}=6.67\times10^{-6}~\mathrm{cm^3s^{-2}g^{-1}}$

(a) 1 kg = 10^{3} g

1 m^{2} = 10^{4} {cm}^{2}

1 kg m^{2} s^{- 2} = 1 kg \times 1 m^{2} \times 1 s^{- 2}

= 10^{3} g \times 10^{4} {cm}^{2} \times 1 s^{- 2} = 10^{7} g {cm}^{2} s^{- 2}

(b) A light-year is the total distance travelled by light in one year.

$\begin{array}{rcl} 1 ly & = & Speed of light \times One year \\ = & (3 \times 10^{8} m / s) \times (365 \times 24 \times 60 \times 60 s) \\ = & 9.46 \times 10^{15} m \\ \Rightarrow 1 m & = & \frac{1}{9.46 \times 10^{15}} = 1.057 \times 10^{- 16} ly \\ (c) 1 m & = & 10^{- 3} km \\ Again, 1 s & = & \frac{1}{3600} h \\ 1 s^{- 1} & = & 3600 h^{- 1} \\ 1 s^{- 2} & = & {(3600)}^{2} h^{- 2} \\ 3 m s^{- 2} & = & (3 \times 10^{- 3} km) \times {(3600)}^{2} h^{- 2} = 3.88 \times 10^{4} km h^{- 2} \\ (d) 1 N & = & 1 kg m s^{- 2} \\ 1 kg & = & 10^{3} g \\ 1 m^{3} & = & 10^{6} {cm}^{3} \\ So, 6.67 \times 10^{- 11} N m^{2} {kg}^{- 2} & = & 6.67 \times 10^{- 11} \times (1 kg m s^{- 2}) (1 m^{2}) (1 {kg}^{- 2}) \\ = & 6.67 \times 10^{- 11} \times (1 {kg}^{- 1} \times 1 m^{3} \times 1 s^{- 2}) \\ = & 6.67 \times 10^{- 11} \times (10^{- 3} g) \times (10^{6} {cm}^{3}) \times (1 s^{- 2}) \\ = & 6.67 \times 10^{- 8} {cm}^{3} s^{- 2} g^{- 1} \end{array}$

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1.	\(1~\mathrm{kgm^2s^{-2}}=10^{7}~\mathrm{gcm^2s^{-2}}\)
2.	\(1~\text m=1.057\times10^{-16}~\text{ly}\)
3.	\(3.0~\mathrm{m/s^2}=10.8~\mathrm{km/h}\)
4.	\(G=6.67\times10^{-11}~\mathrm{Nm^2/kg^2}=6.67\times10^{-6}~\mathrm{cm^3s^{-2}g^{-1}}\)