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• Eight identical spherical liquid drops are each at a potential 2 volt. They coalesce to make one big spherical liquid drop, whose potential is...... a. 1/4 Vb. 16 Vc. 8 Vd. 1/2 V
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• Eight identical spherical liquid drops are each at a potential 2 vol...
Calculating the potential of a big spherical liquid drop after coalescing eight identical spherical liquid drops
Concept: The potential of a charged sphere is given by the equation Vb = Q/4πε₀r, where Vb is the potential, Q is the charge on the sphere, ε₀ is the permittivity of free space, and r is the radius of the sphere.
Step 1: Finding the charge on each sphere: Since all eight spheres are identical, they have the same charge. We can use the equation Vb = Q/4πε₀r to find the charge on one sphere. Rearranging the equation, we get Q = 4πε₀rVb.
Q = 4 x 3.14 x (4x10^-3 m)^2 x 2V
Q = 1.01 x 10^-8 C
Step 2: Finding the charge on the big sphere: When the eight spheres coalesce, their charges add up. Therefore, the charge on the big sphere is eight times the charge on each sphere.
Qbig = 8Q
Qbig = 8 x 1.01 x 10^-8 C
Qbig = 8.08 x 10^-8 C
Step 3: Finding the radius of the big sphere: Since the eight spheres are identical, the big sphere has the same material as the eight spheres. So, the density of the big sphere is eight times the density of each sphere. Therefore, the radius of the big sphere is two times the radius of each sphere.
rbig = 2r
rbig = 2 x 4 x 10^-3 m
rbig = 8 x 10^-3 m
Step 4: Finding the potential of the big sphere: We can use the equation Vb = Q/4πε₀r to find the potential of the big sphere.
Vbig = Qbig/4πε₀rbig
Vbig = (8.08x10^-8 C)/(4πx8.85x10^-12 C²/Nm² x 8x10^-3 m)
Vbig = 2 V
Therefore, the potential of the big spherical liquid drop is 2 V.
Answer: (d) 1/2 V
Concept: The potential of a charged sphere is given by the equation Vb = Q/4πε₀r, where Vb is the potential, Q is the charge on the sphere, ε₀ is the permittivity of free space, and r is the radius of the sphere.
Step 1: Finding the charge on each sphere: Since all eight spheres are identical, they have the same charge. We can use the equation Vb = Q/4πε₀r to find the charge on one sphere. Rearranging the equation, we get Q = 4πε₀rVb.
Q = 4 x 3.14 x (4x10^-3 m)^2 x 2V
Q = 1.01 x 10^-8 C
Step 2: Finding the charge on the big sphere: When the eight spheres coalesce, their charges add up. Therefore, the charge on the big sphere is eight times the charge on each sphere.
Qbig = 8Q
Qbig = 8 x 1.01 x 10^-8 C
Qbig = 8.08 x 10^-8 C
Step 3: Finding the radius of the big sphere: Since the eight spheres are identical, the big sphere has the same material as the eight spheres. So, the density of the big sphere is eight times the density of each sphere. Therefore, the radius of the big sphere is two times the radius of each sphere.
rbig = 2r
rbig = 2 x 4 x 10^-3 m
rbig = 8 x 10^-3 m
Step 4: Finding the potential of the big sphere: We can use the equation Vb = Q/4πε₀r to find the potential of the big sphere.
Vbig = Qbig/4πε₀rbig
Vbig = (8.08x10^-8 C)/(4πx8.85x10^-12 C²/Nm² x 8x10^-3 m)
Vbig = 2 V
Therefore, the potential of the big spherical liquid drop is 2 V.
Answer: (d) 1/2 V
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• Eight identical spherical liquid drops are each at a potential 2 vol...
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• Eight identical spherical liquid drops are each at a potential 2 volt. They coalesce to make one big spherical liquid drop, whose potential is...... a. 1/4 Vb. 16 Vc. 8 Vd. 1/2 V
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• Eight identical spherical liquid drops are each at a potential 2 volt. They coalesce to make one big spherical liquid drop, whose potential is...... a. 1/4 Vb. 16 Vc. 8 Vd. 1/2 V for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about • Eight identical spherical liquid drops are each at a potential 2 volt. They coalesce to make one big spherical liquid drop, whose potential is...... a. 1/4 Vb. 16 Vc. 8 Vd. 1/2 V covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for • Eight identical spherical liquid drops are each at a potential 2 volt. They coalesce to make one big spherical liquid drop, whose potential is...... a. 1/4 Vb. 16 Vc. 8 Vd. 1/2 V.
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