Question

रिक्त स्थानों को मात्रकों के उचित परिर्वतन द्वारा भरिए।
(a) 1 kg $m^{2} s^{-2}$ = ....g $cm^{2} s^{-2}$

(b) 1 m =..... ly

(c) 3.0 m $s^{-2}$ =.... km $h^{-2}$

(d) G= 6.67 × $10^{-11}$1 N $m^{2}$ $(kg)^{-2}$=.... $(cm)^{3} s^{-2} g^{-1}$1.

Answer 1

(a) 10^7 (b) 1.05 × 10^-16 (c) 38880 (d)6.67 × 10^-8

(a) 1kg m²/s² = 10^7 g cm²/s²

explanation : we know, 1kg = 10³ g

1m = 10² cm

so, 1kgm²/s² = (10³g)(10²cm)²/s²

= 10³ × 10⁴ g cm²/s²

= 10^7 g cm²/s²

( b) 1m = 1.05 × 10^-16 light - year

we know, 1light year = 365 × 24 × 3600 × 3 × 10^8 m

= 9.46 × 10^15 m

so, 1m = 1/9.46 × 10^-15 ly

= 1.05 × 10^-16 ly

(c) 3 m/s² = 38880 km/h²

1 m = 10^-3 km

1s = 1/3600 h

so, 3 m/s² = 3 (10^-3 km)/(1/3600 h)²

= 3 × 10^-3 × 1296 × 10⁴ km/h²

= 1296 × 30 km/h²

= 38880 km/h²

(d) G = 6.67 × 10^-11 N/m²/kg² = ..6.67 × 10^-8... cm³/s²/g

1 Nm²/kg² = 1m³/s²/kg

so, 6.67 × 10^-11 (10²cm)³/s²(10³g)

= 6.67 × 10^-11 × 10³ cm³/s²/g

= 6.67 × 10^-8 cm³/s²/g

Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

(a) 1kg m²/s² = 10^7 g cm²/s²

explanation : we know, 1kg = 10³ g

1m = 10² cm

so, 1kgm²/s² = (10³g)(10²cm)²/s²

= 10³ × 10⁴ g cm²/s²

= 10^7 g cm²/s²

( b) 1m = 1.05 × 10^-16 light - year

we know, 1light year = 365 × 24 × 3600 × 3 × 10^8 m

= 9.46 × 10^15 m

so, 1m = 1/9.46 × 10^-15 ly

= 1.05 × 10^-16 ly

(c) 3 m/s² = 38880 km/h²

1 m = 10^-3 km

1s = 1/3600 h

so, 3 m/s² = 3 (10^-3 km)/(1/3600 h)²

= 3 × 10^-3 × 1296 × 10⁴ km/h²

= 1296 × 30 km/h²

= 38880 km/h²

(d) G = 6.67 × 10^-11 N/m²/kg² = ..6.67 × 10^-8... cm³/s²/g

1 Nm²/kg² = 1m³/s²/kg

so, 6.67 × 10^-11 (10²cm)³/s²(10³g)

= 6.67 × 10^-11 × 10³ cm³/s²/g

= 6.67 × 10^-8 cm³/s²/g