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The velocity v of a particle at time t is given by where a, b and c are constant.The dimensions of a, b and c are respectively [2006]
  • a)
    L2, T and LT2
  • b)
    LT2, LT and L
  • c)
    L, LT and T2
  • d)
    LT–2, L and T
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The velocity v of a particle at time t is given bywhere a, b and c are...
V=at+b/t+c

As c is added to t, ∴    [c]=[T]
 
[at]=[LT^−1] or, [a]=[LT-^1]/[T]= [LT−^2]

[b]/[T]= [LT−^1]   ∴[b]=[L].
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Community Answer
The velocity v of a particle at time t is given bywhere a, b and c are...
According to the principle of dimensional homogenity

Dimension of v = dimension of at  =  dimension of t+cb​

Dimension of a =  [t][v]​=TLT−2​=[LT−2]

Dimension of b = [v][t]=[LT−1T]=[L] 

Dimension of c = [t]=[T]
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The velocity v of a particle at time t is given bywhere a, b and c are constant.The dimensions of a, b and c are respectively [2006]a)L2, T and LT2b)LT2, LT and Lc)L, LT and T2d)LT–2, L and TCorrect answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The velocity v of a particle at time t is given bywhere a, b and c are constant.The dimensions of a, b and c are respectively [2006]a)L2, T and LT2b)LT2, LT and Lc)L, LT and T2d)LT–2, L and TCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The velocity v of a particle at time t is given bywhere a, b and c are constant.The dimensions of a, b and c are respectively [2006]a)L2, T and LT2b)LT2, LT and Lc)L, LT and T2d)LT–2, L and TCorrect answer is option 'D'. Can you explain this answer?.
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