A mass m attached to free end of a spring executes SHM with a period of 1 s. If the mass is increased by 3 kg the period of oscillation increases by one second, the value of mass m is kg.

Question

A mass m attached to free end of a spring executes SHM with a period of 1 s. If the mass is increased by 3 kg the period of oscillation increases by one second, the value of mass m is kg. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

T =2 π √( m / k )=1 T prime=2 π √( m +3/ k )=2 ( T / T prime)=√( m / m +3)=(1/2) ⇒ ( m / m +3)=(1/4) m =1

Q. A mass $m$ attached to free end of a spring executes SHM with a period of $1 s$ . If the mass is increased by $3 k g$ the period of oscillation increases by one second, the value of mass $m$ is ______ $k g$ .

$T = 2 π \frac{m}{k} = 1$
$T^{'} = 2 π \frac{m + 3}{k} = 2$
$\frac{T}{T ^{'}} = \frac{m}{m + 3} = \frac{1}{2}$
$\Rightarrow \frac{m}{m + 3} = \frac{1}{4}$
$m = 1$

Q. A mass m attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3kg the period of oscillation increases by one second, the value of mass m is ______kg.

T=2πkm​​=1 T′=2πkm+3​​=2 T′T​=m+3m​​=21​ ⇒m+3m​=41​ m=1

Q. A mass $m$ attached to free end of a spring executes SHM with a period of $1 s$ . If the mass is increased by $3 k g$ the period of oscillation increases by one second, the value of mass $m$ is ______ $k g$ .

$T = 2 π \frac{m}{k} = 1$
$T^{'} = 2 π \frac{m + 3}{k} = 2$
$\frac{T}{T ^{'}} = \frac{m}{m + 3} = \frac{1}{2}$
$\Rightarrow \frac{m}{m + 3} = \frac{1}{4}$
$m = 1$