91. One planet is observed from two diametrically opposite point A and B on the earth the angle subtended at the planet by the two directions of observations is \(1.8^{\circ}\). Given the diameter of the earth to be about \(1.276\times 10^{7}m\). What will be distance of the planet from the earth ?
A. \(40.06\times 10^{8}m\)
B. \(4.06\times 10^{8}m\)
C. \(400.6\times 10^{13}m\)
D. \(11\times 10^{8}m\)
Answer : Option B
Explanation :
\(\theta =1.8^{\circ}=0.01\pi\ rad\)
\(b=1.27\times 10^{7}m\)
\(D=\frac{b}{\theta }=4.06\times 10^{8}m\)
92. Find the distance at which 4 AU would subtend an angle of exactly 1" of arc. \(\left [ 1AU=1.496\times 10^{11}m,1''=4.85\times 10^{16}rad \right ]\)
A. \(1.123\times 10^{5}m\)
B. \(11.23\times 10^{5}m\)
C. \(1.123\times 10^{17}m\)
D. \(11.23\times 10^{17}m\)
Answer : Option C
93. The percentage error in the distance \(100\pm 5\ cm\) is
94. In an experiment to determine the density of a cube the percentage error in the measurement of mass is 0.25 % and the percentage error in the measurement of length is 0.50 % what will be the percentage error in the determination of its density ?
A. 2.75 %
B. 1.75 %
C. 0.75 %
D. 1.25 %
Answer : Option B
Explanation :
\(density(\sigma )=\frac{mass(m)}{volume(l^{3})}\)
Percentage error in density
= \(\left [ \frac{\Delta M}{M}+3\left ( \frac{\Delta L}{L} \right ) \right ]\times 100\)
= 1.75 %
95. If \(A=b^{4}\) the fractional error in A is
A. \(\frac{(\Delta b)^{4}}{b}\)
B. \(\frac{\Delta b}{b}\)
C. \(4\left ( \frac{\Delta b}{b} \right )\)
D. \((\Delta b)^{4}\)
Answer : Option C
96. If \(P=\frac{A^{2}B}{C^{3}}\) where percentage error in A , B and C are respectively \(\pm 2\)%, \(\pm 3\)% and \(\pm 5\)% then total percentage error in measurement of P
A. 18%
B. 14%
C. 21%
D. 12%
Answer : Option C
Explanation :
\(P=\frac{A^{2}B}{C^{3}}\)
\(\frac{\Delta P}{P}\%=\left [ 2\frac{\Delta A}{A}+\frac{\Delta B}{B}+3\frac{\Delta C}{C} \right ]\)
\(=21\%\)
97. In the experiment of simple pendulum error in length of pendulum (\(l\)) is 5 % and that of \(g\) is 3 % then find percentage error in measurement of periodic time for pendulum
A. 4.2%
B. 1.2%
C. 2%
D. 4%
Answer : Option D
Explanation :
\(T=2\pi \sqrt{\frac{l}{g}}\)
\(\frac{\Delta T}{T}\times 100=\left [ \frac{1}{2}\times\frac{\Delta l}{l}+\frac{1}{2}\times\frac{\Delta g}{g} \right ]\times 100\)
\(=4\%\)
98. Acceleration due to gravity is given by \(g=\frac{GM}{R^{2}}\) what is the equation of the fractional error \(\frac{\Delta g}{g}\) in measurement of gravity g ? [G & M constant]
A. \(-\frac{\Delta R}{R}\)
B. \(2\frac{\Delta R}{R}\)
C. \(-2\frac{\Delta R}{R}\)
D. \(\frac{1}{2}\frac{\Delta R}{R}\)
Answer : Option B
99. The period of oscillation of a simple pendulum is given by \(T=2\pi \sqrt{\frac{l}{g}}\) what is the equation of the relative error \(\frac{\Delta T}{T}\) in measurement of period T ?
A. \(\frac{1}{2}\frac{\Delta l}{l}\)
B. \(2\frac{\Delta l}{l}\)
C. \(\frac{1}{4}\frac{\Delta l}{l}\)
D. \(4\frac{\Delta l}{l}\)
Answer : Option A
100. The length of a rod is \((10.15\pm 0.06)cm\) what is the length of two such rods ?
A. \((20.30\pm 0.06)cm\)
B. \((20.30\pm 1.6)cm\)
C. \((10.30\pm 0.12)cm\)
D. \((20.30\pm 0.12)cm\)
Answer : Option D
Explanation :
length of two rods \(=2l\)
\(=2(10.15\pm 0.06)\ cm\)
\(=(20.30\pm 0.12)\ cm\)