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1.Units, Dimensions and Measurement
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વાસ્તવિક એકમમાં જો દળ એકમ બમણું થઈ જાય અને તે સમયના એકમનો અડધો થઈ જાય તો, $8$ જૂલ કાર્યના એકમ .......... બરાબર હશે.
A$6$
B$4$
C$1$
D$10$
Solution
(c)
$\text { Work } \rightarrow\left[ ML ^2 T ^{-2}\right]$
$n_1 V_1=n_2 V_2$
$\frac{(8) M _1 L _1^2 T _1^{-2}}{ M _2 L _2^2 T _2^{-2}}=n_2$
$\Rightarrow 8\left[\frac{ M _1}{ M _2}\right]\left[\frac{ L _1}{ L _2}\right]^2\left[\frac{ T _1}{ T _2}\right]^{-2}=n_2$
$\Rightarrow 8\left[\frac{ M _1}{2 M _1}\right]\left[\frac{ L _1}{ L _1}\right]^2\left[\frac{2 T _1}{ T _1}\right]^{-2}=n_2$
$\Rightarrow 8 \times \frac{1}{2} \times \frac{1}{4}=n_2$
$\Rightarrow n_2=1$
So, unit of 8 joule $=1 \times$ new units
$\text { Work } \rightarrow\left[ ML ^2 T ^{-2}\right]$
$n_1 V_1=n_2 V_2$
$\frac{(8) M _1 L _1^2 T _1^{-2}}{ M _2 L _2^2 T _2^{-2}}=n_2$
$\Rightarrow 8\left[\frac{ M _1}{ M _2}\right]\left[\frac{ L _1}{ L _2}\right]^2\left[\frac{ T _1}{ T _2}\right]^{-2}=n_2$
$\Rightarrow 8\left[\frac{ M _1}{2 M _1}\right]\left[\frac{ L _1}{ L _1}\right]^2\left[\frac{2 T _1}{ T _1}\right]^{-2}=n_2$
$\Rightarrow 8 \times \frac{1}{2} \times \frac{1}{4}=n_2$
$\Rightarrow n_2=1$
So, unit of 8 joule $=1 \times$ new units
Standard 11
Physics
