Q.

The speed of a particle executing SHM is given by the equation v2=144−9x2  then the wrong statements among the following is

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a

Amplitude of the particle is 4 units

b

Time period is π3 units

c

Maximum velocity is 12 units

d

Maximum acceleration is 36 units

answer is B.

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Detailed Solution

maximum velocity in SHM is at x = 0 that is when there is no displacement. Thus putting x = 0, the maximum velocity comes out to be = 12 units V=144−9x2=342−x2 Comparing with the equation V=ωA2−x2  we get  ω=3   and  A=4As a result T = 2π/3  Also we know acceleration =  −ω2x  in the case of SHMFor maximum acceleration x=A=4  which gives us maximum acceleration as 36 units, Hence option 3 is wrong.
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