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question_answer1)
If the acceleration due to gravity is \[10\,m{{s}^{-2}}\] and the units of length and time are changed in kilometer and hour respectively, the numerical value of the acceleration is [Kerala PET 2002]
A)
360000 done
clear
B)
72,000 done
clear
C)
36,000 done
clear
D)
129600 done
clear
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question_answer2)
If \[L,\,C\] and \[R\] represent inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency [IIT 1984]
A)
\[\frac{1}{RC}\] done
clear
B)
\[\frac{R}{L}\] done
clear
C)
\[\frac{1}{\sqrt{LC}}\] done
clear
D)
\[\frac{C}{L}\] done
clear
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question_answer3)
Number of particles is given by \[n=-D\frac{{{n}_{2}}-{{n}_{1}}}{{{x}_{2}}-{{x}_{1}}}\] crossing a unit area perpendicular to X-axis in unit time, where \[{{n}_{1}}\] and \[{{n}_{2}}\] are number of particles per unit volume for the value of \[x\] meant to \[{{x}_{2}}\] and \[{{x}_{1}}\]. Find dimensions of \[D\] called as diffusion constant [CPMT 1979]
A)
\[{{M}^{0}}L{{T}^{2}}\] done
clear
B)
\[{{M}^{0}}{{L}^{2}}{{T}^{-4}}\] done
clear
C)
\[{{M}^{0}}L{{T}^{-3}}\] done
clear
D)
\[{{M}^{0}}{{L}^{2}}{{T}^{-1}}\] done
clear
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question_answer4)
With the usual notations, the following equation \[{{S}_{t}}=u+\frac{1}{2}a(2t-1)\] is
A)
Only numerically correct done
clear
B)
Only dimensionally correct done
clear
C)
Both numerically and dimensionally correct done
clear
D)
Neither numerically nor dimensionally correct done
clear
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question_answer5)
If the dimensions of length are expressed as \[{{G}^{x}}{{c}^{y}}{{h}^{z}}\]; where \[G,\,c\] and \[h\] are the universal gravitational constant, speed of light and Planck's constant respectively, then [IIT 1992]
A)
\[x=\frac{1}{2},\,\,y=\frac{1}{2}\] done
clear
B)
\[x=\frac{1}{2},\,\,z=\frac{1}{2}\] done
clear
C)
\[y=\frac{1}{2},\,\,z=\frac{3}{2}\] done
clear
D)
\[y=-\frac{3}{2},\,\,z=\frac{1}{2}\] done
clear
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question_answer6)
A highly rigid cubical block \[A\] of small mass \[M\] and side \[L\] is fixed rigidly onto another cubical block \[B\]of the same dimensions and of low modulus of rigidity \[\eta \] such that the lower face of \[A\] completely covers the upper face of \[B\]. The lower face of \[B\]is rigidly held on a horizontal surface. A small force \[F\] is applied perpendicular to one of the side faces of \[A\]. After the force is withdrawn block \[A\] executes small oscillations. The time period of which is given by [IIT 1992]
A)
\[2\pi \sqrt{\frac{M\eta }{L}}\] done
clear
B)
\[2\pi \sqrt{\frac{L}{M\eta }}\] done
clear
C)
\[2\pi \sqrt{\frac{ML}{\eta }}\] done
clear
D)
\[2\pi \sqrt{\frac{M}{\eta L}}\] done
clear
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question_answer7)
The pair(s) of physical quantities that have the same dimensions, is (are) [IIT 1995]
A)
Reynolds number and coefficient of friction done
clear
B)
Latent heat and gravitational potential done
clear
C)
Curie and frequency of a light wave done
clear
D)
Planck's constant and torque done
clear
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question_answer8)
The speed of light\[(c)\], gravitational constant \[(G)\] and Planck's constant \[(h)\] are taken as the fundamental units in a system. The dimension of time in this new system should be [AMU 1995]
A)
\[{{G}^{1/2}}{{h}^{1/2}}{{c}^{-5/2}}\] done
clear
B)
\[{{G}^{-1/2}}{{h}^{1/2}}{{c}^{1/2}}\] done
clear
C)
\[{{G}^{1/2}}{{h}^{1/2}}{{c}^{-3/2}}\] done
clear
D)
\[{{G}^{1/2}}{{h}^{1/2}}{{c}^{1/2}}\] done
clear
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question_answer9)
If the constant of gravitation \[(G)\], Planck's constant \[(h)\] and the velocity of light \[(c)\] be chosen as fundamental units. The dimension of the radius of gyration is [AMU (Eng.) 1999]
A)
\[{{h}^{1/2}}{{c}^{-3/2}}{{G}^{1/2}}\] done
clear
B)
\[{{h}^{1/2}}{{c}^{3/2}}{{G}^{1/2}}\] done
clear
C)
\[{{h}^{1/2}}{{c}^{-3/2}}{{G}^{-1/2}}\] done
clear
D)
\[{{h}^{-1/2}}{{c}^{-3/2}}{{G}^{1/2}}\] done
clear
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question_answer10)
\[X=3Y{{Z}^{2}}\] find dimension of \[Y\] in (MKSA) system, if \[X\] and \[Z\] are the dimension of capacity and magnetic field respectively [MP PMT 2003]
A)
\[{{M}^{-3}}{{L}^{-2}}{{T}^{-4}}{{A}^{-1}}\] done
clear
B)
\[M{{L}^{-2}}\] done
clear
C)
\[{{M}^{-3}}{{L}^{-2}}{{T}^{4}}{{A}^{4}}\] done
clear
D)
\[{{M}^{-3}}{{L}^{-2}}{{T}^{8}}{{A}^{4}}\] done
clear
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question_answer11)
In the relation \[P=\frac{\alpha }{\beta }{{e}^{-\frac{\alpha Z}{k\theta }}}\] P is pressure, Z is the distance, k is Boltzmann constant and q is the temperature. The dimensional formula of b will be [IIT (Screening) 2004]
A)
\[[{{M}^{0}}{{L}^{2}}{{T}^{0}}]\] done
clear
B)
\[[{{M}^{1}}{{L}^{2}}{{T}^{1}}]\] done
clear
C)
\[[{{M}^{1}}{{L}^{0}}{{T}^{-1}}]\] done
clear
D)
\[[{{M}^{0}}{{L}^{2}}{{T}^{-1}}]\] done
clear
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question_answer12)
The frequency of vibration of string is given by \[\nu =\frac{p}{2l}{{\left[ \frac{F}{m} \right]}^{1/2}}\]. Here p is number of segments in the string and l is the length. The dimensional formula for m will be [BHU 2004]
A)
\[[{{M}^{0}}L{{T}^{-1}}]\] done
clear
B)
\[[M{{L}^{0}}{{T}^{-1}}]\] done
clear
C)
\[[M{{L}^{-1}}{{T}^{0}}]\] done
clear
D)
\[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\] done
clear
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question_answer13)
Column I Column II (i) Curie \[ML{{T}^{-2}}\] (ii) Light year \[M\] (iii) Dielectric strength Dimensionless (iv) Atomic weight \[T\] (v) Decibel \[M{{L}^{2}}{{T}^{-2}}\] (F) \[M{{T}^{-3}}\] (G) \[{{T}^{-1}}\] (H) \[L\] (I) \[ML{{T}^{-3}}{{I}^{-1}}\] (J) \[L{{T}^{-1}}\] Choose the correct match [IIT 1992]
A)
(i) G, (ii) H, (iii) C, (iv) B, (v) C done
clear
B)
(i) D, (ii) H, (iii) I, (iv) B, (v) G done
clear
C)
(i) G, (ii) H, (iii) I, (iv) B, (v) G done
clear
D)
None of the above done
clear
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question_answer14)
A wire has a mass \[0.3\pm 0.003\,g\], radius \[0.5\pm 0.005\,mm\] and length \[6\pm 0.06\,cm\]. The maximum percentage error in the measurement of its density is [IIT (Screening) 2004]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
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question_answer15)
If 97.52 is divided by 2.54, the correct result in terms of significant figures is
A)
38.4 done
clear
B)
38.3937 done
clear
C)
38.394 done
clear
D)
38.39 done
clear
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