A particle of mass 10 gm is placed in a potential field given by V=(50 x2+100) J / kg. The frequency of oscillation in cycle/sec is

Question

A particle of mass 10 gm is placed in a potential field given by V=(50 x2+100) J / kg. The frequency of oscillation in cycle/sec is (A) (10/π) (B) (5/π) (C) (100/π) (D) (50/π)

Tardigrade Admin · Accepted Answer

Potential energy U=m V ⇒ U=(50 x2+100) 10-2 F=-(d U/d x)=-(100 x) 10-2 ⇒ m ω2 x=-(100 × 10-2) x 10 × 10-3 ω2 x=100 × 10-2 x ⇒ ω2=100 ∴ ω=10 ⇒ f=(ω/2 π)=(10/2 π)=(5/π)

Q. A particle of mass $10 g m$ is placed in a potential field given by $V = (50 x^{2} + 100) J / k g$ . The frequency of oscillation in cycle/sec is

$\frac{10}{π}$

$\frac{5}{π}$

$\frac{100}{π}$

$\frac{50}{π}$

Q. A particle of mass 10gm is placed in a potential field given by V=(50x2+100)J/kg. The frequency of oscillation in cycle/sec is

π10​

π5​

π100​

π50​

Potential energy U=mV ⇒U=(50x2+100)10−2 F=−dxdU​=−(100x)10−2 ⇒mω2x=−(100×10−2)x 10×10−3ω2x=100×10−2x ⇒ω2=100∴ω=10 ⇒f=2πω​=2π10​=π5​

Q. A particle of mass $10 g m$ is placed in a potential field given by $V = (50 x^{2} + 100) J / k g$ . The frequency of oscillation in cycle/sec is

$\frac{10}{π}$

$\frac{5}{π}$

$\frac{100}{π}$

$\frac{50}{π}$