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Question : 1 of 33
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(a) The volume of a cube of side 1 cm is equal to ....m3^{3}.
(b) The surface area of a solid cylinder of radius 2.0 cm and height 10 cm is equal to ....(mm)2^{2}.
(c) A vehicle moving with a speed of 18 km h1^{-1} covers....m in 1 s.
(d) The relative density of lead is 11.3. Its density is ....g cm3^{-3} or ...kg m3^{-3}.
Solution:  
(a) The volume of a cube of side 1 cm is given by, V=(1cm)3V = (1\,\text{cm})^{3}
or V=(102m)3=106m3V = (10^{-2}\,\text{m})^{3}=10^{-6}\,\text{m}^{3}.
(b) The surface area of a solid cylinder of radius r and height h is givenby :
A=A= Area of two caps ++ curved surface area
=2πr2+2πrh=2πr(r+h)=2\pi r^{2}+2\pi r h=2\pi r(r+h)
here r=2cm=20mm,r = 2\,\text{cm} = 20\,\text{mm},
h=10cm=100mmh = 10\,\text{cm} = 100\,\text{mm}
A=2×227×20(20+100)mm2\therefore A = 2\times\frac{22}{7}\times 20(20+100)\,\text{mm}^{2}
=15086mm2=15086\,\text{mm}^{2}
=1.5086×104mm2=1.5086\times 10^{4}\,\text{mm}^{2}
=1.5×104mm2=1.5\times10^{4}\,\text{mm}^{2}
(c) Here v=18kmh1v=18\,\text{km}\,\text{h}^{-1}
=18×1000m3600s=5ms1=\frac{18\times1000\,\text{m}}{3600\,\text{s}}=5\,\text{m}\,\text{s}^{-1}
t=1s, x=vt=5×1=5mt=1\,\text{s},\ x=v t=5\times1=5\,\text{m}
(d) Relative density of lead = 11.3, density of water = 1 g cm3^{-3}
We know that relative density of lead =density of leaddensity of water=\frac{\text{density of lead}}{\text{density of water}}
\therefore density of lead = relative density of lead × density of water
=11.3×1gcm3=11.3\times 1\,\text{g}\,\text{cm}^{-3}
=11.3gcm3=11.3\,\text{g}\,\text{cm}^{-3}
Also in S.I. system density of water = 103^{3}kg m3^{-3}
\therefore density of lead =11.3×103kgm3=11.3\times 10^{3}\,\text{kg}\,\text{m}^{-3}
=1.13×104kgm3=1.13\times10^{4}\,\text{kg}\,\text{m}^{-3}
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