A block is placed on a horizontal platform. The system is making horizontal oscillations about a fixed point with a frequency of $0.5 H z$ . The maximum amplitude of oscillation if the block is not to slide on the horizontal platform is (coefficient of friction between the block and the platform is $0.4$ )

0.1 m

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0.2 m

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0.3 m

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0.4 m

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Solution

The correct option is D $0.4 m$
$f = K x$
condition of just sliding
$μ N = m ω^{2} A$
$μ m g = m ω^{2} A$
$ω^{2} A = μ g$
$ω = 2 π f$
$ω = π$
$∴ π^{2} A = 0.4 \times g$
$A = 0.4 m$

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A block is placed on a horizontal platform. The system is making horizontal oscillations about a fixed point with a frequency of 0.5Hz. The maximum amplitude of oscillation if the block is not to slide on the horizontal platform is (coefficient of friction between the block and the platform is 0.4)

The correct option is D 0.4mf=Kxcondition of just sliding μN=mω2Aμmg=mω2Aω2A=μgω=2πfω=π∴π2A=0.4×gA=0.4m

The correct option is D $0.4 m$
$f = K x$
condition of just sliding
$μ N = m ω^{2} A$
$μ m g = m ω^{2} A$
$ω^{2} A = μ g$
$ω = 2 π f$
$ω = π$
$∴ π^{2} A = 0.4 \times g$
$A = 0.4 m$