You visited us 485 times! Enjoying our articles? Unlock Full Access!

Center of Mass as an Average Point

A spring bala...

Question

A spring balance has a scale that reads from $0$ to $50$ kg. The length of the scale is $20$ cm. A block of mass m is suspended from this balance, when displaced and released, it oscillates with a period $0.5$ s. The value of m is (Take g = 10 m $s^{- 2})$

8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

12

No worries! We‘ve got your back. Try BYJU‘S free classes today!

16

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

20

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $16$ kg
The $20$ cm length of the scaler reads upto $50$ kg.
$∴ F = m g = (50 k g) (10 m s^{- 2}) = 500 N$ and $x = 20 c m = 0.2 m$
$∴$ Spring constant, $k = \frac{F}{x} = \frac{500 N}{0.2 m} = 2500 N m^{- 1}$
As $T = 2 π \sqrt{\frac{m}{k}}$
Squaring both sides, we get
$T^{2} = \frac{4 π^{2} m}{k}$
$m = \frac{T^{2} k}{4 π} = \frac{(0.5 s)^{2} \times (2500 N m^{- 1})}{4 \times (3.14)^{2}} = 16 k g$

Suggest Corrections

Similar questions

A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body?

Q. A spring balance has a scale that reads

0

50 k g .

The length of the scale is

20 c m .

A body suspended from this balance, when displaced an released, oscillates with period of

0.6 s e c .

What is the mass of the body?
(

g = 10 m s^{- 2}

)

Q. A spring balance has a scale that reads from

0

50 kg

. The length of the scale is

20 cm

. A body suspended from his balance, when displaced and released, oscillates with a period of

0.6 s

. What is the weight of the body ? (Assume that

π^{2} = 10, g = 10 {m/s}^{2}

)

Q. A spring balance has a scale reading from 0 to 50 kg. The length of the scale is 20 cm. A body suspended to the spring balance when displaced and released oscillates with a period of

0.6

second. The mass off the body is:

Q. A spring balance has a scale that can read from

0 t o 50 k g

. The length of the scale is

20 c m

. A body suspended from this balance when displaced and released oscillates harmonically with a time period of

0.6 s

. The mass of the body is

(t a k e g = 10 m / s^{2})

Join BYJU'S Learning Program

A spring balance has a scale that reads from 0 to 50kg. The length of the scale is 20cm. A block of mass m is suspended from this balance, when displaced and released, it oscillates with a period 0.5s. The value of m is (Take g = 10 m s−2)

The correct option is C 16kgThe 20cm length of the scaler reads upto 50kg.∴F=mg=(50kg)(10ms−2)=500N and x=20cm=0.2m∴ Spring constant, k=Fx=500N0.2m=2500Nm−1As T=2π√mkSquaring both sides, we getT2=4π2mkm=T2k4π=(0.5s)2×(2500Nm−1)4×(3.14)2=16kg

A spring balance has a scale that reads from $0$ to $50$ kg. The length of the scale is $20$ cm. A block of mass m is suspended from this balance, when displaced and released, it oscillates with a period $0.5$ s. The value of m is (Take g = 10 m $s^{- 2})$