Question

A box has sides 10 cm, 20 cm and 15 cm. If its weight is 5 N, find the pressure exerted
by the box when it is placed on its (i) largest face and (ii) smallest face.

Answer 1

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❚ QuEstiOn ❚

# A box has sides 10 cm, 20 cm and 15 cm. If its weight is 5 N, find the pressure exerted by the box when it is placed on its

(i) largest face .

&

(ii) smallest face.

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❚ ANsWeR ❚

✺ Fig :

$\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\thicklines\put(5.6,5.6){ A }\put(11.1,5.8){ B }\put(11.08,8.9){ C }\put(5.46,8.7){ D }\put(3.55,10.15){ E }\put(3.55,7.15){ F }\put(9.14,10.235){ H }\put(9.14,7.3){ G }\put(3.3,6.3){ 15\:cm }\put(7.75,6.2){ 20\:cm }\put(11.1,7.5){ 10\:cm }\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

✺ Given :

• Length ( l ) = 20 cm
• Breadth (b) = 15 cm
• Height (h) = 10 cm
• weight (w) = 5 N

✺ To Find :

The pressure exerted by the box when it is placed on its

• largest face .
• smallest face.

✺ Explanation :

➩ Case :1 ( placed on its largest face)

The largest face is = ABGF

with sides 20 cm × 15 cm.

$\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\thicklines\put(3.3,6.3){ 15\:cm }\put(7.75,6.2){ 20\:cm }\put(11.1,7.5){ 10\:cm }\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

✺ Therefore :

✏ Area of the face ABGF or CDEH

= ( 20 ×15 ) cm²

= 300 cm²

= 0.3 m²

∴ Pressure exerted by the box when it is placed on its largest face is ,

= weight / area

= (5/0.3) N/m²

= 16.67 N/m² (almost)

= 16.67 Pascal

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➩ Case :2 ( placed on its smallest face)

The largest face is = ADEF or BCHG

with sides 15 cm × 10 cm.

$\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\thicklines\put(3.3,6.3){ 10\:cm }\put(7.75,6.2){ 15\:cm }\put(11.1,7.5){ 20\:cm }\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

✺ Therefore :

✏ Area of the face ADEF

= ( 10 ×15 ) cm²

= 150 cm²

= 0.15 m²

∴ Pressure exerted by the box when it is placed on its smallest face is

= weight / area

= (5/0.15) N/m²

= 33.33 N/m² (almost)

= 33.33 Pascal

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