A mass M, attached to a spring, oscillates with a period of 2 s. If the mass is increased by 4 kg, the time period increases by 1 s. Assuming that Hooke's law is obeyed, the initial mass M was

Question

A mass M, attached to a spring, oscillates with a period of 2 s. If the mass is increased by 4 kg, the time period increases by 1 s. Assuming that Hooke's law is obeyed, the initial mass M was (A) 3.2 kg (B) 1 kg (C) 2 kg (D) 8 kg

Tardigrade Admin · Accepted Answer

As , T=2=2 π √(M/k) 2+1=2 π √(M+4/k) (from questions) or 3=2 π √(k+4/k) So, (4/9)=(M/M+4) or 4 M+16=9 M or M=(16/5)=3.2 kg

Q. A mass $M$ , attached to a spring, oscillates with a period of $2 s$ . If the mass is increased by $4 k g$ , the time period increases by 1 s. Assuming that Hooke's law is obeyed, the initial mass $M$ was

3.2 kg

1 kg

2 kg

8 kg

$A s, T = 2 = 2 π \frac{M}{k}$
$2 + 1 = 2 π \frac{M + 4}{k}$ (from questions)
or $3 = 2 π \frac{k + 4}{k}$
So, $\frac{4}{9} = \frac{M}{M + 4}$
or $4 M + 16 = 9 M$
or $M = \frac{16}{5} = 3.2 k g$

Q. A mass M, attached to a spring, oscillates with a period of 2s. If the mass is increased by 4kg, the time period increases by 1 s. Assuming that Hooke's law is obeyed, the initial mass M was