A particle of mass 10 g is undergoing S.H.M. of amplitude 10 cm and period 0.1 s. The maximum value of force on particle is about

Question

A particle of mass 10 g is undergoing S.H.M. of amplitude 10 cm and period 0.1 s. The maximum value of force on particle is about (A) 5.6 N (B) 2.75 N (C) 3.5 N (D) 4 N

Tardigrade Admin · Accepted Answer

T=0.1 m=0.01 kg ∴ ω =20 π rad / s Amplitude A=0.1 m a=-ω2 x Maximum acceleration =-ω2 A Maximum force =-m ω2 A F max =-0.01 ×(20 π)2 × 0.1 F max =-0.001 × 400 π2 =-3.95 N or -4 N approximately

Q. A particle of mass $10 g$ is undergoing S.H.M. of amplitude $10 c m$ and period $0.1 s$ . The maximum value of force on particle is about

5.6 N

2.75 N

3.5 N

4 N

$T = 0.1 m = 0.01 k g$
$∴ ω = 20 π r a d / s$
Amplitude $A = 0.1 m$
$a = - ω^{2} x$
Maximum acceleration $= - ω^{2} A$
Maximum force $= - m ω^{2} A$
$F_{m a x} = - 0.01 \times (20 π)^{2} \times 0.1$
$F_{m a x} = - 0.001 \times 400 π^{2}$
$= - 3.95 N$
or $- 4 N$ approximately

Q. A particle of mass 10g is undergoing S.H.M. of amplitude 10cm and period 0.1s. The maximum value of force on particle is about

5.6 N

2.75 N

3.5 N

4 N

T=0.1m=0.01kg ∴ω=20πrad/s Amplitude A=0.1m a=−ω2x Maximum acceleration =−ω2A Maximum force =−mω2A Fmax​=−0.01×(20π)2×0.1 Fmax​=−0.001×400π2 =−3.95N or −4N approximately

Q. A particle of mass $10 g$ is undergoing S.H.M. of amplitude $10 c m$ and period $0.1 s$ . The maximum value of force on particle is about

$T = 0.1 m = 0.01 k g$
$∴ ω = 20 π r a d / s$
Amplitude $A = 0.1 m$
$a = - ω^{2} x$
Maximum acceleration $= - ω^{2} A$
Maximum force $= - m ω^{2} A$
$F_{m a x} = - 0.01 \times (20 π)^{2} \times 0.1$
$F_{m a x} = - 0.001 \times 400 π^{2}$
$= - 3.95 N$
or $- 4 N$ approximately