1
IIT-JEE 2008 Paper 1 Offline
+3
-1

Student I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different length of the pendulum and/or record time for different number of oscillations. The observations area shown in the table.

Least count for length = 0.1 cm

Least count for time = 0.1 s

Student Length of the
pendulum
(cm)
No. of
oscillations
(n)
Total time
for(n)
oscillations
(s)
Time
periods
(s)
I 64.0 8 128.0 16.0
II 64.0 4 64.0 16.0
III 20.0 4 36.0 9.0

If EI, EII and EIII are the percentage errors in g, i.e., $$\left(\frac{\triangle g}g\times100\right)$$ for students I, II and III, respectively,then

A
EI = 0
B
EI is minimum
C
EI = EII
D
EII is maximum
2
IIT-JEE 2007
+6
-1.5
Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II.

Column I

(A) GMeMs ,
G $$\to$$ universal gravitational constant, Me $$\to$$ mass of the earth, Ms $$\to$$ mass of the Sun

(B) $${{3RT} \over M}$$,
R $$\to$$ universal gas constant, T $$\to$$ absolute temperature, M $$\to$$ molar mass

(C) $${{{F^2}} \over {{q^2}{B^2}}}$$ ,
F $$\to$$ force, q $$\to$$ charge, B $$\to$$ magnetic field

(D) $${{G{M_e}} \over {{R_e}}}$$,
G $$\to$$ universal gravitational constant, Me $$\to$$ mass of the earth, Re $$\to$$ radius of the earth

Column II

(p) (volt) (coulomb) (metre)

(q) (kilogram) (metre)3 (second)−2

(r) (meter)2(second)−2

A
A $$\to$$ (p) & (q), B $$\to$$ (r) & (s), C $$\to$$ (r) & (s), D $$\to$$ (r) & (s)
B
A $$\to$$ (p), B $$\to$$ (r) & (s), C $$\to$$ (r) & (s), D $$\to$$ (r) & (s)
C
A $$\to$$ (p) & (q), B $$\to$$ (r) & (s), C $$\to$$ (r) & (s), D $$\to$$ (r)
D
A $$\to$$ (p) & (q), B $$\to$$ (r), C $$\to$$ (r) & (s), D $$\to$$ (r) & (s)
3
IIT-JEE 2007 Paper 2 Offline
+3
-1

A student performs an experiment to determine the Young's modulus of a wire, exactly 2 m long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of $$\pm0.05\;\mathrm{mm}$$ at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of $$\pm0.01\;\mathrm{mm}$$. Take g = 9.8 m/s2 (exact). The Young's modulus obtained from the reading is

A
$$\left(2.0\;\pm\;0.3\right)\times10^{11}\;\mathrm N/\mathrm m^2$$
B
$$\left(2.0\;\pm\;0.2\right)\times10^{11}\;\mathrm N/\mathrm m^2$$
C
$$\left(2.0\;\pm\;0.1\right)\times10^{11}\;\mathrm N/\mathrm m^2$$
D
$$\left(2.0\;\pm\;0.05\right)\times10^{11}\;\mathrm N/\mathrm m^2$$
4
IIT-JEE 2006
+3
-0.75
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
$$\begin{array}{l}\triangle\mathcal l\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\triangle\mathrm T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm n\\1\;\mathrm{mm}\;\;\;\;\;\;\;\;\;\;\;\;0.1\;\sec\;\;\;\;\;\;\;\;\;\;\;\;50\end{array}$$
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