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1.Units, Dimensions and Measurement
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નીચે દર્શાવેલ કઇ જોડનાં પરિમાણો સમાન નથી?
Aબળ અને બળનો આઘાત
Bકોણીય વેગમાન અને પ્લાન્ક અચળાંક
Cઊર્જા અને ટોર્ક
Dસ્થિતિસ્થાપક અંક અને દબાણ
(AIPMT-2000)
Solution
$\text { For (A): }\text { Energy }= kg \cdot m ^2 \cdot s ^2=\left[ ML ^2 T ^{-2}\right]$
$\text { Torque }= kg \cdot m ^2 \cdot s ^2=\left[ ML ^2 T ^{-2}\right]$
$\text { For (B) : }\text { Force }= kg \times m / s ^2=\left[ MLT ^{-2}\right]$
$\text { Impulse }= kgm / s =\left[ MLT ^{-1}\right]$
$\text { For (C) : }\text { Angular momentum }= kgm ^2 / s =\left[ ML ^2 T ^{-1}\right]$
$\text { Planck's constant }= kgm ^2 / s =\left[ ML ^2 T ^{-1}\right]$
$\text { For (D) : }\text { Elastic modulus }= kg / m ^2=\left[ ML ^{-2}\right]$
$\text { Pressure }= kg / m ^2=\left[ ML ^{-2}\right]$
From the above data, only Force and Impulse does not have equal dimensions.
$\text { Torque }= kg \cdot m ^2 \cdot s ^2=\left[ ML ^2 T ^{-2}\right]$
$\text { For (B) : }\text { Force }= kg \times m / s ^2=\left[ MLT ^{-2}\right]$
$\text { Impulse }= kgm / s =\left[ MLT ^{-1}\right]$
$\text { For (C) : }\text { Angular momentum }= kgm ^2 / s =\left[ ML ^2 T ^{-1}\right]$
$\text { Planck's constant }= kgm ^2 / s =\left[ ML ^2 T ^{-1}\right]$
$\text { For (D) : }\text { Elastic modulus }= kg / m ^2=\left[ ML ^{-2}\right]$
$\text { Pressure }= kg / m ^2=\left[ ML ^{-2}\right]$
From the above data, only Force and Impulse does not have equal dimensions.
Standard 11
Physics