Question

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Answer 1

Correct Question:-

• A book of mass 2 kg placed on a table of mass 20 kg. Bottom of  each of four legs of table are in circular shape. If the pressure acting on ground due to table is 7000 Pa, then the radius of bottom of leg is:

Solution:-

Mass of book is 2kg and Mass of table is 20 kg so,

→ the total mass, m = 2 kg + 20 kg = 22 kg

Calculating the force exerted by this total mass on the ground. (F =?)

→ Force exerted = mass × acceleration

→ F = m a

[ We will take 'a' as acceleration due to gravity here ]

→ F = 22 × 9.8 N

Given that,

→  the total force acting on the ground is, P = 7000 Pa

Now since

Bottom of each of 4 legs of table are circular.., so Let the area of each circular base be 'A  m²'

then,

→  the total area in contact with the ground will be = 4A  m²

Using formula

→ Pressure = force / Area

→ P = F / (4A)

→ 7000 = ( 22 × 9.8 ) / (4A)

→ 4A = ( 22 × 9.8 ) / 7000

→ A = ( 22 × 9.8 ) / ( 7000 × 4 )

→ A = 0.0077 m²

Let, the radius of each circular base be 'r'

then,

→ A = π r²

→ 0.0077 = 22/7 × r²

→ r² = 0.00245

→ r² = 245/100000

→ r = 0.049 m = 0.05 m  [approx.]

Therefore,

• Radius of each circular base will be 0.05 metres (approximately).

Answer 2

Given:-

$\bigstar$A book of mass 2 kg placed on a table of mass 20 kg.

$\bigstar$Bottom of each of four legs of table are in circular shape.

$\bigstar$Pressure = 7000 pa

To Find:-

$\bigstar$The radius of bottom of leg is?...

Solution:-

$\bigstar$Total mass of the book and table is 22kg..

To Find Force:-

$\bigstar$Using formula,

$\longrightarrow { \boxed{ \boxed{ \boxed{ \bold{Force = Mass \times Acceleration}}}}}$

$\longrightarrow \bold{ \: F \: = 22 \times 9.8 \: N}$

To Find Area :-

$\bigstar$Area of each leg of a table be A then, Area of 4 leg of a table be 4A.

$\bigstar$Using Formula,

$\\ \longrightarrow { \boxed{ \boxed{ \boxed{ \bold{Pressure = \frac{Force}{Area}}}}}}$

$\\ \longrightarrow\bold {7000 = \frac{22 \times 9.8}{4A } }$

$\\ \longrightarrow\bold{4A = \frac{22 \times 9.8}{7000} }$

$\\ \longrightarrow\bold {A \: = \frac{22 \: \times \: 9.8 }{7000 \times 4} = 0.0077 \: {m}^{2} }$

To Find radius :-

$\bigstar$The Area of each circular leg be r.

$\bigstar$Using Formula,

$\longrightarrow { \boxed{ \boxed{ \boxed{ \bold{ Area \: of \: circular \: leg= \pi \: {r}^{2} }}}}}$

$\\ \longrightarrow \bold {0.0077 = \frac{22}{7} \times {r}^{2} }$

$\\ \longrightarrow \bold{ {r}^{2} = 0.00245}$

$\\ \longrightarrow \bold{r = \sqrt{ 0.00245}}$

$\\ \longrightarrow \bold{ r = 0.049 \: m}$

$\bigstar$The radius of the each circular leg is 0.049 m