A force of 6.4 N stretches a vertical spring by 0.1 m. The mass that must be suspended from the spring so that it oscillates with a time period of π / 4 second.

Question

A force of 6.4 N stretches a vertical spring by 0.1 m. The mass that must be suspended from the spring so that it oscillates with a time period of π / 4 second. (A) (π/4) kg (B) (4/π) kg (C) 1 kg (D) 10 kg

Tardigrade Admin · Accepted Answer

Spring constant K=(6.4/0.1)=64 N / m. Now T=2 π √(m/k) or (π/4)=2 π √(m/64) ∴ m=1 kg

Q. A force of $6.4 N$ stretches a vertical spring by $0.1 m$ . The mass that must be suspended from the spring so that it oscillates with a time period of $π /4$ second.

$\frac{π}{4} k g$

$\frac{4}{π} k g$

$1 k g$

$10 k g$

Spring constant $K = \frac{6.4}{0.1} = 64 N / m$ .
Now $T = 2 π \frac{m}{k}$
or $\frac{π}{4} = 2 π \frac{m}{64} ∴ m = 1 k g$

Q. A force of 6.4N stretches a vertical spring by 0.1m. The mass that must be suspended from the spring so that it oscillates with a time period of π/4 second.

4π​kg

π4​kg

1kg

10kg