1

IIT-JEE 2006

MCQ (Single Correct Answer)
A student performs an experiment for determination of $$\mathrm g\left(=\frac{4\mathrm\pi^2\mathcal l}{\mathrm T^2}\right)$$. The error in length $$\mathcal l$$ is $$\triangle\mathcal l$$ and in the time T is $$\triangle\mathrm T$$ and n is number of times the reading is taken.The reading of g is most accurate for
A
$$\begin{array}{l}\triangle\mathcal l\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\triangle\mathrm T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm n\\5\;\mathrm{mm}\;\;\;\;\;\;\;\;\;\;\;\;0.2\;\sec\;\;\;\;\;\;\;\;\;\;\;\;10\end{array}$$
B
$$\begin{array}{l}\triangle\mathcal l\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\triangle\mathrm T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm n\\5\;\mathrm{mm}\;\;\;\;\;\;\;\;\;\;\;\;0.2\;\sec\;\;\;\;\;\;\;\;\;\;\;\;20\end{array}$$
C
$$\begin{array}{l}\triangle\mathcal l\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\triangle\mathrm T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm n\\5\;\mathrm{mm}\;\;\;\;\;\;\;\;\;\;\;\;0.1\;\sec\;\;\;\;\;\;\;\;\;\;\;\;10\end{array}$$
D
$$\begin{array}{l}\triangle\mathcal l\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\triangle\mathrm T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm n\\1\;\mathrm{mm}\;\;\;\;\;\;\;\;\;\;\;\;0.1\;\sec\;\;\;\;\;\;\;\;\;\;\;\;50\end{array}$$
2

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)
Which of the following set have different dimensions?
A
Pressure, Young's modulus, Stress
B
EMF, Potential difference, Electric potential
C
Heat, Work done, Energy
D
Dipole moment, Electric flux, Electric field
3

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)
A wire of length $$l = 6 \pm 0.06$$ cm and $$r = 0.5 \pm 0.005$$ cm and mass $$m = 0.3 \pm 0.003$$ gm. Maximum percentage error in density is
A
4
B
2
C
1
D
6.8
4

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)
Pressure depends on distance as, $$P = {\alpha \over \beta }\exp \left( { - {{\alpha z} \over {k\theta }}} \right)$$, where $$\alpha $$, $$\beta $$ are constants, z in distance, k is Boltzman's constant and $$\theta $$ is temperature. The dimention of $$\beta $$ are
A
[M0L0T0]
B
[M-1L-1T-1]
C
[M0L2T0]
D
[M-1L1T2]

Explanation

The given expression is

$$P = {\alpha \over \beta }\exp \left( { - {{\alpha z} \over {k\theta }}} \right)$$

Now,

$$[z] = [{L^1}]$$

$$[\theta ] = [{K^1}]$$

$$[k] = [{M^1}{L^2}{T^{ - 2}}{K^{ - 1}}]$$

Since the terms which are raised to power in an exponential function are dimensionless, we get

$$[\alpha] = \left[ {{{k\theta } \over z}} \right] = [{M^1}{L^1}{T^{ - 2}}]$$

Also, $$[P] =$$ $$\left[ {{\alpha \over \beta }} \right]$$

$$ \Rightarrow $$ $$\left[ \beta \right] = \left[ {{\alpha \over P}} \right]$$

$$ \Rightarrow $$ $$\left[ \beta \right] = \left[ {{{{M^1}{L^1}{T^{ - 2}}} \over {M{L^{ - 1}}{T^{ - 2}}}}} \right]$$ = $$[{M^0}{L^2}{T^0}]$$

Answer (C)

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