Question

(39)Two metallic spheres of radii 1 cm and 2 cm are given charges 10-2 C and 5 * 10-2 C respectively. If they are connected by a conducting wire, the final charge on the smaller sphere is (1) 3 × 10-2 C (2) 2* 10-2 C (3) 1 * 10-2 C (4) 6 × 10-20

NEET/Medical Exams

Physics

Solution

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Correct option (d) ( 2 times 10^{-2} mathrm{C} ) Explanation: Radii of sphere ( left(mathrm{R}_{1}right)=1 mathrm{cm}=1 times 10^{-2} mathrm{m}: ) ( left(R_{2}right)=2 mathrm{cm}=2 times 10^{-2} mathrm{m} ) and charges on sphere; ( left(Q_{1}right)=10^{-2} mathrm{C} ) and ( left(Q_{2}right)=5 times 10^{-2} mathrm{C} ) Common potential ( (V)=frac{text { Total charge }}{text { Total capacity }}=frac{Q_{1}+Q_{2}}{C_{1}+C_{2}} ) [ =frac{left(1 times 10^{-2}right)+left(5 times 10^{-2}right)}{4 pi varepsilon_{0} 10^{-2}+4 pi varepsilon_{0}left(2 times 10^{-2}right)}=frac{6 times 10^{-2}}{4 pi varepsilon_{0}left(3 times 10^{-2}right)} ] Therefore final charge on smaller sphere ( left(C_{1} Vright) ) [ =4 pi varepsilon_{0} times 10^{-2} times frac{6 times 10^{-2}}{4 pi varepsilon_{0} times 3 times 10^{-2}}=2 times 10^{-2} mathrm{C} ]