1

### IIT-JEE 2008

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

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

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

In a screw gauge, the zero of main scale coincides with the fifth division of circular scale in figure (i).The circular division of screw gauge is 50. It moves 0.5 mm on main scale in one rotation.The diameter of the ball in figure (ii) is

A
2.25 mm
B
2.20 mm
C
1.20 mm
D
1.25 mm