1

### IIT-JEE 2011

The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2 %, the relative percentage error in the density is
A
0.9 %
B
2.4 %
C
3.1 %
D
4.2 %
2

### IIT-JEE 2010

A vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is
A
0.02 mm
B
0.05 mm
C
0.1 mm
D
0.2 mm
3

### 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
4

### 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)