141. Write the dimensional formula of r.m.s (root mean square) speed.
A. \(M^{1}L^{2}T^{-2}\)
B. \(M^{0}L^{2}T^{-2}\)
C. \(M^{0}L^{1}T^{-1}\)
D. \(M^{1}L^{0}T^{-1}\)
Answer : Option C
Explanation :
\(U_{rms}=\sqrt{u^{2}} = \) root mean square speed
142. One physical quantity represented by an equation as \(\frac{\pi }{2}(p-q)c\) where p, q and c are length then quantity is
A. Length
B. Velocity
C. Area
D. Volume
Answer : Option C
Explanation :
If \(p = q = c = L\)
then \((p - q)c = L^{2} =\) Area
143. The dimensional formula of magnetic flux is
A. \(M^{1}L^{2}T^{-2}A^{-1}\)
B. \(M^{1}L^{2}T^{1}A^{2}\)
C. \(M^{1}L^{2}T^{-2}A^{2}\)
D. \(M^{-1}L^{-2}T^{1}A^{2}\)
Answer : Option A
144. Which physical quantity has unit of pascal - second ?
A. Force
B. Energy
C. Coefficient of viscocity
D. Velocity
Answer : Option C
Explanation :
\(F=nA\frac{\mathrm{d} v}{\mathrm{d} x}\)
\(\therefore n=\frac{F}{A\frac{\mathrm{d} v}{\mathrm{d} x}}=\) pascal second
145. Dimensional formula of CV ? where C - capacitance and V - potential different
A. \(M^{1}L^{-2}T^{4}A^{2}\)
B. \(M^{1}L^{2}T^{-3}A^{1}\)
C. \(M^{0}L^{0}T^{1}A^{-1}\)
D. \(M^{0}L^{0}T^{1}A^{1}\)
Answer : Option D
146. The equation of a wave is given by \(Y=A\sin \omega \left [ \frac{x}{v}-k \right ]\) where \(\omega \) is the angular velocity and \(v\) is the linear velocity. Write the dimensional formula of \(K\)
A. \(M^{0}L^{0}T^{1}\)
B. \(M^{1}L^{0}T^{-1}\)
C. \(M^{0}L^{1}T^{1}\)
D. \(M^{1}L^{-1}T^{1}\)
Answer : Option A
Explanation :
\(y=A\sin \omega \left [ \frac{x}{v}-k \right ]\)
\(\therefore \frac{x}{v}=k\)
\(k=\frac{x}{v}=M^{^{0}}L^{0}T^{1}\)
147. If p and q are different physical quantities then which one of following is only possible dimensionally ?
148. From \(\left ( P+\frac{a}{v^{2}} \right )\left ( V-b \right )=constant \) equation is dimensionally correct find the dimensional formula for b ? where p = pressure v = volume
A. \(M^{0}L^{3}T^{0}\)
B. \(M^{1}L^{3}T^{0}\)
C. \(M^{0}L^{1}T^{3}\)
D. \(M^{1}L^{1}T^{1}\)
Answer : Option A
Explanation :
\(\left ( P+\frac{a}{v^{2}} \right )\left ( V-b \right )=constant \)
\(PV-Pb+\frac{a}{v}-\frac{ab}{v^{2}}=constant \)
\(\therefore PV-Pb\)
\(\therefore V=b=M^{0}L^{3}T^{0}\)
149. Pressure \(P=A\cos Bx+C\sin Dt\) where \(x\) in meter and \(t\) in time then find dimensional formula of \(\frac{D}{B}\)
A. \(M^{1}L^{1}T^{-1}\)
B. \(M^{0}L^{1}T^{-1}\)
C. \(M^{1}L^{1}T^{0}\)
D. \(M^{-1}L^{0}T^{1}\)
Answer : Option B
Explanation :
\(\cos Bx = dimentionless\)
\(Bx = M^{0}L^{0}T^{0}\)
\(B = \frac{M^{0}L^{0}T^{0}}{x}=M^{0}L^{-1}T^{0}\)
Same as \(D = M^{0}L^{0}T^{-1}\)
\(\therefore \frac{D}{B} = M^{0}L^{1}T^{-1}\)
150. Find the dimensional formula for energy per unit surface area per unit time
A. \(M^{1}L^{0}T^{-2}\)
B. \(M^{0}L^{1}T^{-1}\)
C. \(M^{1}L^{0}T^{-3}\)
D. \(M^{1}L^{-1}T^{1}\)
Answer : Option C