A baseball has mass 143 g and speed 45.0 m/s, with the speedknown to within 0.10

Question

A baseball has mass 143 g and speed 45.0 m/s, with the speedknown to within 0.100%. What is the minimum uncertainty in the position of thebaseball? A) 1.56 x 10^-32 m B) 1.65 x 10^-32 m C) 1.56 x 10^-30 m D) 1.65 x 10^-30 m A baseball has mass 143 g and speed 45.0 m/s, with the speedknown to within 0.100%. What is the minimum uncertainty in the position of thebaseball? A) 1.56 x 10^-32 m B) 1.65 x 10^-32 m C) 1.56 x 10^-30 m D) 1.65 x 10^-30 m A baseball has mass 143 g and speed 45.0 m/s, with the speedknown to within 0.100%. What is the minimum uncertainty in the position of thebaseball? A) 1.56 x 10^-32 m B) 1.65 x 10^-32 m C) 1.56 x 10^-30 m D) 1.65 x 10^-30 m

Explanation / Answer

Mass m = 143 g = 0.143 kg

Velocity v = 45 m / s

Momentum P = mv = 6.435 kg m / s

Uncertanity in momentum   dP = 0.1% of P = 6.435* 10 ^-3 kg m / s

                                                  

                                          

Frm Uncertanity principle dP * dx = h / [ 2(pi) ]

From this uncertainty in position   dx = h / [ 2(pi) *dP]

Where h = planck’s constant = 6.625 *10^-34 J s

Plug the values we get dx = 1.65 * 10 ^ -32 m

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