Q: In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is 10 ± 0 . 1 cm and the distance of its real image from the lens is

Given: Object distance = 10 ± 0 . 1 cm Image distance = 20 ± 0 . 2 cm As per lens formula 1 v - 1 u = 1 f . . . i ⇒ 1 20 - 1 - 10 = 1 f ⇒ f = 20 3 cm Differentiate equation i on both sides, we get - 1 v 2 d v - - 1 u 2 d u = - 1 f 2 d f For calculating maximum error, we will add all values ⇒ 1 f 2 d f = + 1 v 2 d v + 1 u 2 d u ⇒ d f f × 100 = 0 . 2 20 2 + 0 . 1 10 2 20

Question 1

Length, breadth and thickness of a strip having a uniform cross section are measured to be 10.5 cm , 0.05 mm , and 6.0 ~m , respectively. Which of the following option(s) give(s) the volume of the str

Accepted Answer

L =10.5 ~cm 3 significant digits b =0.05 ~cm 1 significant digit t =6.0 ~m 2 significant digits Volume, V = Lbt must have only 1 significant digit aligned & V =10.5 0.05 10^ -1 6.0 10^ -4 ~cm ^3 \ & =3 10^ -5 cc aligned

Question 2

The dimensions of a cone are measured using a scale with a least count of 2 ~mm . The diameter of the base and the height are both measured to be 20.0 ~cm . The maximum percentage error in the determi

Accepted Answer

V = 1 3 ( D 2 )^2 H \% Error in V =2 (% error in D )+\% error in H . Least count is 2 ~mm . \% error in D = 2 ~mm 20 ~cm 100 \%=1 \% & % error in H = 2 ~mm 20 ~cm 100 \%=1 \% So \% error in V =2 1 \%+1 \%=3 \%

Question 3

In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is 10 &#177; 0 . 1 &#160; cm and the distance of its real image from the lens is

Accepted Answer

Given: Object distance = 10 &#177; 0 . 1 &#160; cm Image distance = 20 &#177; 0 . 2 &#160; cm As per lens formula 1 v - 1 u = 1 f &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; . . . i &#8658; 1 20 - 1 - 10 = 1 f &#8658; &#160; f = 20 3 &#160; cm Differentiate equation i  on both sides, we get - 1 v 2 d v - - 1 u 2 d u = - 1 f 2 d f For calculating maximum error, we will add all values &#8658; 1 f 2 d f = + 1 v 2 d v + 1 u 2 d u &#8658; d f f &#215; 100 = 0 . 2 20 2 + 0 . 1 10 2 20

Question 4

Two capacitors with capacitance values C 1 = 2000 &#177; 10 &#160; pF   and  C 2 = 3000 &#177; 15 &#160; pF  are connected in series. The voltage applied across this combination is&nbsp

Accepted Answer

For the purpose of calculation of error, fundamental formula is considered 1 C = 1 C 1 + 1 C 2 &#8658; C = 1200 &#160; p F - d C C 1 2 = - d C 1 C 1 2 - d C 2 C 2 2 d C = 6 &#160; p F Equivalent capacitance = 1200 &#177; 6 &#160; pF E = 1 / 2 &#160; CV 2 ( d E / E = d C / C + 2 d V / V ) &#215; 100 = 1 . 3 %

Mathematics in Physics — Previous Year Questions & Solutions