Physics, asked by dikshyajps, 5 hours ago

the density p of earth depends upon the radius r , the acceleration due to gravity g on the surface of the earth and the gravitational constant G . Derive a relation between them using dimensional method.​

Answers

Answered by raushankumar82715785
0

Explanation:

Answer:

Given :

➠ Density of Metal

➱ 7.8 g/cm³

➠ External diameter of metal pipe

➱ 10 cm

▶ External radius

➻ diameter /2

➻ 10 cm / 2

➠ External radius = 5 cm

▶ Height of pipe ➠ 35 cm

➠ Thickness = 1 cm

__________________________

To Find :

➠ The mass of the pipe given

➠ Volume of metal used in pipe

__________________________

Formula to be applied :

▶Internal radius

➠ External Radius - Thickness

__________________________

Solution :

➠ Place given value in formula

➠ r = R - 1 cm

\tt{Internal \: radius }Internalradius

\rm{\implies \: 5 \: cm \: - 1cm \: }⟹5cm−1cm

\bf{\implies \: r = \: 4 \: cm}⟹r=4cm

__________________________

Formula to be applied :

▶ External volume of pipe

➠ π R² h

__________________________

➠ Place given value in formula

\tt{External \: Volume}ExternalVolume

\rm{ \: \frac{22}{7} \times( {5)}^{2} \times 35 }

7

22

×(5)

2

×35

\rm{ \: \frac{22}{7} \times 25\times 35 }

7

22

×25×35

\rm{ \: \frac{22 \times 25 \times 35}{7} }

7

22×25×35

\rm{ \frac{19250}{7} }

7

19250

\bf{2750}2750

__________________________

Formula to be applied :

▶ External volume of pipe

➠ π r² h

__________________________

➠ Place given value in formula

\tt{External \: Volume}ExternalVolume

\rm{ \: \frac{22}{7} \times( {4)}^{2} \times 35 }

7

22

×(4)

2

×35

\rm{ \: \frac{22}{7} \times16 \times 35 }

7

22

×16×35

\rm{ \: \frac{22 \times 16 \times 35}{7} }

7

22×16×35

\rm{ \: \frac{12320}{7} }

7

12320

\bf{1760}1760

__________________________

Formula to be applied :

▶ Volume of metal used in pipe

➠( External volume of pipe - Internal volume of pipe)

__________________________

➠ Place given value in formula

\tt{2750 -1760}2750−1760

\bf{990 \: cm³}990cm³

__________________________

Given :

➠ Mass of 1 cm³ of metal is 7.8 gram

__________________________

Final Answer :

➠Therefore mass of pipe

➠ mass of 990 cm ³ metal

= 990 × 7.8 gram

\bf{➠7.722 \: kg}➠7.722kg

Similar questions