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Write the dimension of coefficient of viscosity.
Answer: The dimensional formula is [M L⁻¹ T⁻¹].
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A ball is thrown up. What is its velocity and acceleration at the top?
Answer: Velocity = 0; Acceleration = 9.8 m/s² (downward).
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Name two physical quantities whose dimensions are the same.
Answer: Work and Energy ([M L² T⁻²]).
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If x = at + bt², where x is in meters and t in seconds, what are the units of a and b?
Answer: Units of a = m/s, Units of b = m/s².
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When do we say two vectors are orthogonal? Check the correctness of the relation |2GM/R|.
Answer: Vectors are orthogonal if their dot product is zero. The relation |2GM/R| is dimensionally correct as it matches the dimensions of velocity [L T⁻¹].
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A force is inclined at 60° to the horizontal. If the horizontal component of the force is 40 N, calculate the vertical component.
Answer: Vertical component = 40 × √3 ≈ 69.3 N.
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At what angle should a stone be thrown to get the maximum horizontal range?
Answer: 45°.
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What is the angle of projection at which Hmax and Range are equal?
Answer: 76° (approximately).
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What will be the effect on the horizontal range of a projectile when its initial speed is doubled, keeping its angle of projection the same?
Answer: The range will become 4 times the original.
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A unit vector is represented by ai + bj + ck. If the values of a and b are 0.6 and 0.8, respectively, find the value of c.
Answer: c = 0.
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What will be the nature of the velocity-time graph for uniform motion?
Answer: A straight horizontal line.
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The position coordinate of a moving particle is given by x = 6 + 18t + 9t² (x in meters and t in seconds). What is its velocity at t = 2s?
Answer: Velocity = 54 m/s.
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When is the sum of two vectors maximum, and when is it minimum?
Answer: Maximum when vectors are in the same direction; Minimum when vectors are in opposite directions.
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What is the unit for the spring (force) constant?
Answer: N/m (Newton per meter).
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What is the elastic potential energy stored in a spring?
Answer: U = (1/2)kx², where k = spring constant, x = displacement.
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A mass m collides with another mass 2m and sticks to it. What is the nature of the collision?
Answer: Perfectly inelastic collision.