SATHEE: Physics And Measurement Question 203

Physics And Measurement Question 203

Question: Force F is given in terms of time $t$ and distance $x$ by F =A sin C $t$ + B cos $D x$ . Then the dimensions of $A / B$ and $C / D$ are

Options:

A) $[M_{}^{0} L_{}^{0} T_{}^{0}], [M_{}^{0} L_{}^{0} T_{}^{- 1}]$

B) $[M_{}^{} L_{}^{} T_{}^{- 2}], [M_{}^{0} L_{}^{- 1} T_{}^{0}]$

C) $[M_{}^{0} L_{}^{0} T_{}^{0}], [M_{}^{0} L_{}^{} T_{}^{- 1}]$

D) $[M_{}^{0} L_{}^{1} T_{}^{- 1}], [M_{}^{0} L_{}^{0} T_{}^{0}]$

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Answer:

Correct Answer: C

Solution:

[c] $\frac{A}{B} = \frac{F o r c e}{F o r c e} = [M^{0} L^{0} T^{0}]$ Ct = angle

$\Rightarrow$ $C = \frac{A n g l e}{T i m e} = \frac{1}{T} = T^{- 1}$ Dx = angle

$\Rightarrow$ $D = \frac{A n g l e}{D i s \tan c e} = \frac{1}{L} = L^{- 1}$

$∴ \frac{C}{D} = \frac{T^{- 1}}{L^{- 1}} = [M^{0} L T^{- 1}]$

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Physics And Measurement Question 203

Question: Force F is given in terms of time t and distance x by F =A sin C t + B cos Dx . Then the dimensions of A/B and C/D are

Options:

Answer:

Solution:

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Question: Force F is given in terms of time $t$ and distance $x$ by F =A sin C $t$ + B cos $D x$ . Then the dimensions of $A / B$ and $C / D$ are