1.

If force (F). velocity (V) and time (T) are taken asfundamental units, then the dimensions of massare[AIPMT-2014](1) [F V T-](2) [F VT(3) [FV-T'(4) [F V-T]​

Answer» <html><body><p></p><p><img align="absmiddle" alt="\maltese \: \underline{\sf AnsWer :} \: \maltese \\" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%5Cmaltese%20%5C%3A%20%5Cunderline%7B%5Csf%20AnsWer%20%3A%7D%20%5C%3A%20%5Cmaltese%20%5C%5C%20" title="\maltese \: \underline{\sf AnsWer :} \: \maltese \\"/></p><p><img align="absmiddle" alt="\dashrightarrow\:\:\sf m \propto [F]^{x} \: [V]^{y} \: [T]^{z} \\" class="latex-formula" id="TexFormula2" src="https://tex.z-dn.net/?f=%5Cdashrightarrow%5C%3A%5C%3A%5Csf%20m%20%5Cpropto%20%5BF%5D%5E%7Bx%7D%20%20%5C%3A%20%5BV%5D%5E%7By%7D%20%5C%3A%20%20%5BT%5D%5E%7Bz%7D%20%5C%5C%20" title="\dashrightarrow\:\:\sf m \propto [F]^{x} \: [V]^{y} \: [T]^{z} \\"/></p><p>By adding <strong>'k' </strong>as a proportionality constant we get :</p><p></p><p></p><p><img align="absmiddle" alt="\dashrightarrow\:\:\sf m = k \: [F]^{x} \: [V]^{y} \: [T]^{z} \\" class="latex-formula" id="TexFormula3" src="https://tex.z-dn.net/?f=%5Cdashrightarrow%5C%3A%5C%3A%5Csf%20m%20%20%3D%20k%20%5C%3A%20%20%5BF%5D%5E%7Bx%7D%20%20%5C%3A%20%5BV%5D%5E%7By%7D%20%5C%3A%20%20%5BT%5D%5E%7Bz%7D%20%5C%5C" title="\dashrightarrow\:\:\sf m = k \: [F]^{x} \: [V]^{y} \: [T]^{z} \\"/></p><p><img align="absmiddle" alt="\\\bullet\textsf{ Dimensions of mass (m) =\textbf{[M$^ \text1$L$^ \text0$T$^ \text0$]}} \\" class="latex-formula" id="TexFormula4" src="https://tex.z-dn.net/?f=%5C%5C%5Cbullet%5Ctextsf%7B%20Dimensions%20of%20mass%20%28m%29%20%3D%5Ctextbf%7B%5BM%24%5E%20%5Ctext1%24L%24%5E%20%5Ctext0%24T%24%5E%20%5Ctext0%24%5D%7D%7D%20%5C%5C%20" title="\\\bullet\textsf{ Dimensions of mass (m) =\textbf{[M$^ \text1$L$^ \text0$T$^ \text0$]}} \\"/></p><p><img align="absmiddle" alt="\bullet\textsf{ Dimensions of force (F) = [M] [LT$^{ \text{-2}}$] = \textbf{[MLT$^{ \text{-2}}$]}} \\" class="latex-formula" id="TexFormula5" src="https://tex.z-dn.net/?f=%5Cbullet%5Ctextsf%7B%20Dimensions%20of%20force%20%28F%29%20%3D%20%5BM%5D%20%5BLT%24%5E%7B%20%5Ctext%7B-2%7D%7D%24%5D%20%20%3D%20%20%5Ctextbf%7B%5BMLT%24%5E%7B%20%5Ctext%7B-2%7D%7D%24%5D%7D%7D%20%5C%5C%20" title="\bullet\textsf{ Dimensions of force (F) = [M] [LT$^{ \text{-2}}$] = \textbf{[MLT$^{ \text{-2}}$]}} \\"/></p><p><img align="absmiddle" alt="\bullet\textsf{ Dimensions of velocity (V) = $\dfrac{ \text{[L]}}{ \text{[T]}}$ = \textbf{[M$^\text0$LT$^{ \text{-1}}$]}} \\" class="latex-formula" id="TexFormula6" src="https://tex.z-dn.net/?f=%5Cbullet%5Ctextsf%7B%20Dimensions%20of%20velocity%20%28V%29%20%3D%20%24%5Cdfrac%7B%20%5Ctext%7B%5BL%5D%7D%7D%7B%20%5Ctext%7B%5BT%5D%7D%7D%24%20%3D%20%20%5Ctextbf%7B%5BM%24%5E%5Ctext0%24LT%24%5E%7B%20%5Ctext%7B-1%7D%7D%24%5D%7D%7D%20%5C%5C%20" title="\bullet\textsf{ Dimensions of velocity (V) = $\dfrac{ \text{[L]}}{ \text{[T]}}$ = \textbf{[M$^\text0$LT$^{ \text{-1}}$]}} \\"/></p><p><img align="absmiddle" alt="\bullet\textsf{ Dimensions of Time Period (T) =\textbf{[M$^ \text0$L$^ \text0$T$^ \text1$]}}\\ \\" class="latex-formula" id="TexFormula7" src="https://tex.z-dn.net/?f=%5Cbullet%5Ctextsf%7B%20Dimensions%20of%20Time%20Period%20%28T%29%20%3D%5Ctextbf%7B%5BM%24%5E%20%5Ctext0%24L%24%5E%20%5Ctext0%24T%24%5E%20%5Ctext1%24%5D%7D%7D%5C%5C%20%20%5C%5C%20" title="\bullet\textsf{ Dimensions of Time Period (T) =\textbf{[M$^ \text0$L$^ \text0$T$^ \text1$]}}\\ \\"/></p><p></p><p></p><p><img align="absmiddle" alt="\dashrightarrow\:\:\sf [M^1 L^0 T^0] = [M^1 L^1 T^{-2}]^{x} \: [M^0 L^1 T^{-1}]^{y} \: [M^0 L^0 T^1]^{z} \\" class="latex-formula" id="TexFormula8" src="https://tex.z-dn.net/?f=%5Cdashrightarrow%5C%3A%5C%3A%5Csf%20%5BM%5E1%20L%5E0%20T%5E0%5D%20%3D%20%20%20%5BM%5E1%20L%5E1%20T%5E%7B-2%7D%5D%5E%7Bx%7D%20%20%5C%3A%20%5BM%5E0%20L%5E1%20T%5E%7B-1%7D%5D%5E%7By%7D%20%5C%3A%20%20%5BM%5E0%20L%5E0%20T%5E1%5D%5E%7Bz%7D%20%5C%5C" title="\dashrightarrow\:\:\sf [M^1 L^0 T^0] = [M^1 L^1 T^{-2}]^{x} \: [M^0 L^1 T^{-1}]^{y} \: [M^0 L^0 T^1]^{z} \\"/></p><p><img align="absmiddle" alt="\dashrightarrow\:\:\sf [M^1 L^0 T^0] = [M]^{x} \: [ L]^{x + y} \: [T]^{ - 2x - y + z} \\" class="latex-formula" id="TexFormula9" src="https://tex.z-dn.net/?f=%5Cdashrightarrow%5C%3A%5C%3A%5Csf%20%5BM%5E1%20L%5E0%20T%5E0%5D%20%3D%20%20%20%5BM%5D%5E%7Bx%7D%20%20%5C%3A%20%5B%20L%5D%5E%7Bx%20%2B%20y%7D%20%5C%3A%20%20%5BT%5D%5E%7B%20-%202x%20-%20y%20%2B%20z%7D%20%5C%5C" title="\dashrightarrow\:\:\sf [M^1 L^0 T^0] = [M]^{x} \: [ L]^{x + y} \: [T]^{ - 2x - y + z} \\"/></p><p></p><p>Now, on <a href="https://interviewquestions.tuteehub.com/tag/comparing-2531631" style="font-weight:bold;" target="_blank" title="Click to know more about COMPARING">COMPARING</a> the <a href="https://interviewquestions.tuteehub.com/tag/powers-1162174" style="font-weight:bold;" target="_blank" title="Click to know more about POWERS">POWERS</a> of LHS and RHS we get :</p><p></p><p><img align="absmiddle" alt="\longrightarrow\:\:\sf x = 1 \qquad \qquad...(i)\\" class="latex-formula" id="TexFormula10" src="https://tex.z-dn.net/?f=%5Clongrightarrow%5C%3A%5C%3A%5Csf%20x%20%3D%201%20%20%5Cqquad%20%5Cqquad...%28i%29%5C%5C%20" title="\longrightarrow\:\:\sf x = 1 \qquad \qquad...(i)\\"/></p><p><img align="absmiddle" alt="\longrightarrow\:\:\sf x + y = 0 \\" class="latex-formula" id="TexFormula11" src="https://tex.z-dn.net/?f=%5Clongrightarrow%5C%3A%5C%3A%5Csf%20x%20%2B%20y%20%3D%200%20%5C%5C%20" title="\longrightarrow\:\:\sf x + y = 0 \\"/></p><p>From equation (i) Substituting x = 1 in above equation we get :</p><p><img align="absmiddle" alt="\longrightarrow\:\:\sf 1 + y = 0 \\" class="latex-formula" id="TexFormula12" src="https://tex.z-dn.net/?f=%5Clongrightarrow%5C%3A%5C%3A%5Csf%201%20%2B%20y%20%3D%200%20%5C%5C%20" title="\longrightarrow\:\:\sf 1 + y = 0 \\"/></p><p><img align="absmiddle" alt="\longrightarrow\:\:\sf y = - 1 \qquad \qquad.... (ii)" class="latex-formula" id="TexFormula13" src="https://tex.z-dn.net/?f=%5Clongrightarrow%5C%3A%5C%3A%5Csf%20y%20%3D%20%20-%201%20%5Cqquad%20%5Cqquad....%20%28ii%29" title="\longrightarrow\:\:\sf y = - 1 \qquad \qquad.... (ii)"/></p><p><img align="absmiddle" alt="\longrightarrow\:\:\sf - 2x - y + z = 0 \\" class="latex-formula" id="TexFormula14" src="https://tex.z-dn.net/?f=%5Clongrightarrow%5C%3A%5C%3A%5Csf%20%20-%202x%20-%20y%20%2B%20z%20%3D%200%20%5C%5C%20%20" title="\longrightarrow\:\:\sf - 2x - y + z = 0 \\"/></p><p>From equation (i) and (ii) Substituting the <a href="https://interviewquestions.tuteehub.com/tag/value-1442530" style="font-weight:bold;" target="_blank" title="Click to know more about VALUE">VALUE</a> of x and y in above equation:</p><p></p><p><img align="absmiddle" alt="\longrightarrow\:\:\sf - 2(1) - ( -1 ) + z = 0 \\" class="latex-formula" id="TexFormula15" src="https://tex.z-dn.net/?f=%5Clongrightarrow%5C%3A%5C%3A%5Csf%20%20-%202%281%29%20-%20%28%20-1%20%29%20%2B%20z%20%3D%200%20%5C%5C%20" title="\longrightarrow\:\:\sf - 2(1) - ( -1 ) + z = 0 \\"/></p><p><img align="absmiddle" alt="\longrightarrow\:\:\sf - 2 + 1 + z = 0 \\" class="latex-formula" id="TexFormula16" src="https://tex.z-dn.net/?f=%5Clongrightarrow%5C%3A%5C%3A%5Csf%20%20-%202%20%20%2B%201%20%20%2B%20z%20%3D%200%20%5C%5C%20" title="\longrightarrow\:\:\sf - 2 + 1 + z = 0 \\"/></p><p><img align="absmiddle" alt="\longrightarrow\:\:\sf - 2 + 1 = - z\\" class="latex-formula" id="TexFormula17" src="https://tex.z-dn.net/?f=%5Clongrightarrow%5C%3A%5C%3A%5Csf%20%20-%202%20%20%2B%201%20%20%3D%20%20-%20z%5C%5C%20" title="\longrightarrow\:\:\sf - 2 + 1 = - z\\"/></p><p><img align="absmiddle" alt="\longrightarrow\:\:\sf - 1 = - z\\" class="latex-formula" id="TexFormula18" src="https://tex.z-dn.net/?f=%5Clongrightarrow%5C%3A%5C%3A%5Csf%20%20-%201%20%20%3D%20%20-%20z%5C%5C%20" title="\longrightarrow\:\:\sf - 1 = - z\\"/></p><p><img align="absmiddle" alt="\longrightarrow\:\:\sf z = 1\\" class="latex-formula" id="TexFormula19" src="https://tex.z-dn.net/?f=%5Clongrightarrow%5C%3A%5C%3A%5Csf%20%20z%20%3D%201%5C%5C%20" title="\longrightarrow\:\:\sf z = 1\\"/></p><p>Hence, our <a href="https://interviewquestions.tuteehub.com/tag/final-461168" style="font-weight:bold;" target="_blank" title="Click to know more about FINAL">FINAL</a> answer will be :</p><p></p><p><img align="absmiddle" alt="\dashrightarrow\:\: \underline{ \boxed{\frak{m = [F]^{1} \: [V]^{-1} \: [T]^{1}}}} \\" class="latex-formula" id="TexFormula20" src="https://tex.z-dn.net/?f=%5Cdashrightarrow%5C%3A%5C%3A%20%5Cunderline%7B%20%5Cboxed%7B%5Cfrak%7Bm%20%3D%20%20%5BF%5D%5E%7B1%7D%20%20%5C%3A%20%5BV%5D%5E%7B-1%7D%20%5C%3A%20%20%5BT%5D%5E%7B1%7D%7D%7D%7D%20%5C%5C" title="\dashrightarrow\:\: \underline{ \boxed{\frak{m = [F]^{1} \: [V]^{-1} \: [T]^{1}}}} \\"/></p><p>Hence,the <a href="https://interviewquestions.tuteehub.com/tag/option-25810" style="font-weight:bold;" target="_blank" title="Click to know more about OPTION">OPTION</a> (4) is correct answer.</p></body></html>


Discussion

No Comment Found

Related InterviewSolutions