Question

A block of wood is kept on a table top.The mass of the wooden block is 5kg and its dimensions are 40cm×20cm×10cm. Find the pressure exerted by the wooden block on the tabletop if it is made to lie on the table top with its sides of dimensions (a) 20cm×10cm and (b)40cm×20cm

Answer 1

a. 30 cm

b. 80 cm


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Answer 2

Given :

• The mass of the wooden block = 5kg
• The dimensions = 40cm × 20cm × 10cm

To Find :

• Pressure exerted by a and b side.

Solution :

✰Here, the weight of the wooden block applies a thrust on the table top. That is,

$\qquad \quad {:} \longrightarrow \sf{\bf{Force \: = \: Mass \: \times \: Gravity }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Force \: = \: 5kg \: \times \: 9.8m \: {s}^{ - 2} }}$

$\qquad \quad {:} \longrightarrow \sf \red{\sf{Force \: = \: 49N }}$

${:} \longrightarrow \sf{\bf{Area \: of \: Side \: = \: Length \: \times \: Breadth }}$

${:} \longrightarrow \sf{\bf{Area \: of \: Side \: = \: 20cm \: \times \: 10cm }}$

${:} \longrightarrow \sf \red{\sf{Area \: of \: Side \: = \: 200cm \: = \: 0.02m^{2} }}$

$\quad{\underline{\boxed{\mathcal{\pmb{\quad Pressure \: = \: \dfrac{Thrust}{Area} \quad}}}}}$

${:} \longrightarrow \sf{\sf{Pressure \: = \: \dfrac{49N}{0.02m^{2}} }}$

${:} \longrightarrow \sf \red{\sf{Pressure \: = \: 2450N \: m^{-2} }}$

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✰ When the block lies on its side of dimensions 40cm × 20cm, it exerts the same thrust .

$\qquad \quad {:} \longrightarrow \sf{\bf{Area \: of \: Side \: = \: Length \: \times \: Breadth }}$

$\qquad \quad{:} \longrightarrow \sf{\bf{Area \: of \: Side \: = \: 40cm \: \times \: 20cm }}$

$\qquad \quad{:} \longrightarrow \sf \blue{\sf{Area \: of \: Side \: = \: 800cm \: = \: 0.08m^{2} }}$

$\quad{\underline{\boxed{\mathcal{\pmb{\quad Pressure \: = \: \dfrac{Thrust}{Area} \quad}}}}}$

${:} \longrightarrow \sf{\sf{Pressure \: = \: \dfrac{49N}{0.08m^{2}} }}$

${:} \longrightarrow \sf \blue{\sf{Pressure \: = \: 612.5N \: m^{-2} }}$

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Therefore :

• The pressure exerted by the side 20cm × 10 cm is 2450N m^-2 and by the side 40 × 20cm is 612.5 N m^-2

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