The potential energy of a particle varies with distance x from a fixed origin as V=A√xx+B where A and B are constants. The dimensions of AB are
A
[M1L5/2T−2]
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B
[M1L2T−2]
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C
[M3/2L5/2T−2]
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D
[M1L7/2T−2]
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Solution
The correct option is D[M1L7/2T−2] As B is added to x so, [B]=[x]=[L] Also, [A√x]=[Vx]or[A=V√x]=ML2T−2L1/2=ML5/2T−2 Thus, [AB]=(ML5/2T−2)(L)=[M1L7/2T−2]