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General
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Question

Block A of mass m is placed over a wedge B of same mass m. Assuming all surfaces to be smooth. The displacement of block A in 1 s if the system is released from rest is

  1. fraction numerator open parentheses 1 plus sin squared space theta close parentheses over denominator open parentheses 1 minus sin squared space theta close parentheses end fraction
  2. fraction numerator g sin space theta over denominator 2 end fraction
  3. g space fraction numerator cos squared begin display style space end style theta over denominator 1 plus sin squared space theta end fraction
  4. g fraction numerator sin squared begin display style space end style theta over denominator 1 plus sin squared space theta end fraction

The correct answer is: g fraction numerator sin squared begin display style space end style theta over denominator 1 plus sin squared space theta end fraction

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A light string fixed at one end to a clamp on ground passes over a fixed pulley and hangs at the other side. It makes an angle of  with the ground. A monkey of mass 5 kg climbs up the rope. The clamp can tolerate a vertical force of 40 N only. The maximum acceleration in upward direction with which the monkey can climb safely is (neglect friction and take straight g equals 10 straight m divided by straight s squared
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An inclined plane makes an angles  with the horizontal. A groove OA=5m cut in the plane makes an angle  with OX. A short smooth cylinder is free to slide down the influence of gravity. The time taken by the cylinder to reach from A to O is open parentheses straight q equals 10 straight m divided by straight s squared close parentheses

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The general value of theta satisfies the equation Tan space theta Tan space open parentheses 120 to the power of ring operator plus theta close parentheses Tan space open parentheses 120 to the power of ring operator minus theta close parentheses equals fraction numerator 1 over denominator square root of 3 end fraction is

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A block of weight W is suspended by a string of fixed length. The ends of the string are held at various positions as shown in the figures below. In which case, if any, is the magnitude of the tension along the string largest?

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If 11 sin squared space x plus 7 Cos squared space x equals 8 then x = - ....

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Or, 11 sin2x + 7 ( 1 - sin2x) = 8 .
Or, 11 sin2x + 7 - 7sin2x = 8 .
Or, 11sin2x - 7 sin2x = 8 - 7 .
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Or, sin2x = 1/4
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Or, Tan (2x - 1 ) = 1 .
Or, Tan x = 1 .
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Or, Tan (2x - 1 ) = 1 .
Or, Tan x = 1 .
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