Given that the displacement of an oscillating particle is given by $y = A s i n [B x + C t + d]$ . The dimensional formula for (ABCD) is:

M^{0} L^{- 1} T^{0}

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M^{0} L^{0} T^{- 1}

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M^{0} L^{- 1} T^{- 1}

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M^{0} L^{0} T^{0}

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Solution

The correct option is D $M^{0} L^{0} T^{- 1}$
Every terms inside the bracket of sin should be dimensionless.
$B x = M^{0} L^{0} T^{0}$
$\Rightarrow B = M^{0} L^{- 1} T^{0}$
$L t = M^{0} L^{0} T^{0}$
$C = M^{0} L^{0} T^{- 1}$
$D = M^{0} L^{0} T^{0}$
$A = M^{0} L^{1} T^{0}$
$A B C D = (L^{1}) (L^{- 1}) (T^{- 1}) (M^{0} L^{0} T^{0}) = M^{0} L^{0} T^{- 1}$

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Similar questions

Given that the displacement of an oscillating particle is given by $y = A sin[Bx + Ct + D]$ . The dimension formula for ABCD is (where x is displacement and t is time)

Q. Match List I with II and select the correct answer:

List-I	List-II
A.Spring constant	1. $M^{1} L^{2} T^{- 2}$
B.pascal	2. $M^{0} L^{0} T^{- 1}$
C.hertz	3. $M^{1} L^{0} T^{- 2}$
D.joule	4. $M^{1} L^{- 1} T^{- 2}$

Q. Match List I with List II and select the correct answer.

List - I	List - II
A) Spring constant	I) [ $M^{1} L^{2} T^{- 2}$ ]
B) Pascal	II) [ $M^{0} L^{0} T^{- 1}$ ]
C) Hertz	III)[ $M^{1} L^{0} T^{- 2}$ ]
D) Joule	IV) [ $M^{1} L^{- 1} T^{- 2}$ ]

Q. Write the SI unit of the physical quantity having following dimensional formula

[M^{0} L^{2} T^{- 2} K^{- 1}]

Q. A rope of mass

m_{0}

and length L is suspended vertically. If a mass m is suspended from the bottom of the rope, find the time for a transverse wave to travel the length of the rope.

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Given that the displacement of an oscillating particle is given by y=Asin[Bx+Ct+d]. The dimensional formula for (ABCD) is:

The correct option is D M0L0T−1Every terms inside the bracket of sin should be dimensionless.Bx=M0L0T0⇒B=M0L−1T0Lt=M0L0T0C=M0L0T−1D=M0L0T0A=M0L1T0ABCD=(L1)(L−1)(T−1)(M0L0T0)=M0L0T−1

Given that the displacement of an oscillating particle is given by $y = A s i n [B x + C t + d]$ . The dimensional formula for (ABCD) is: