Physics

Spring Mass Systems

170 Questions

A spring mass system is a key physics concept used to study oscillations and simple harmonic motion. It involves understanding spring constants, damping, and series or parallel combinations. These principles are frequently tested in engineering entrance examinations.

Series and parallel springsSpring constant calculationsDamped oscillationsSpring compression energyElevator systems

Spring Mass Systems Questions

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A body of mass m is tied to one of a spring and whirled round in a horizontal plane with a constant angular velocity and elongation in the spring is 1 cm. If the angular velocity is doubled, the elongation in the spring becomes 5 cm. The original length of spring is 

  1. 20 cm

  2. 25 cm

  3. 10 cm

  4. 15 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The centripetal force is provided by the spring force: m * omega^2 * (r + x) = k * x, where r is the original length and x is the elongation. For omega, x1 = 1 cm. For 2 * omega, x2 = 5 cm. Thus, m * omega^2 * (r + 1) = k * 1 and m * (2 * omega)^2 * (r + 5) = k * 5. Dividing the equations: 4 * (r + 5) / (r + 1) = 5. Solving for r: 4r + 20 = 5r + 5, so r = 15 cm.

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A wire of length l , area of cross section A  and young's modules of elasticity  y is  suspended from the roof of a building. A  block of mass m is attached at lower end of the wire. if the block is displaced from its mean position and then released the block starts  oscillating. Time period of these oscillation will be

  1. $2\pi \sqrt { \frac { Al }{ mY } } $
  2. $2\pi \sqrt { \frac { AY }{ ml } } $
  3. $2\pi \sqrt { \frac { ml }{ YA } } $
  4. $2\pi \sqrt { \frac { m }{ YAl } } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When a block of mass m is suspended from an elastic wire of length l, area A, and Young's modulus Y, the effective spring constant of the wire is k = YA / l. The time period of vertical oscillations of the mass-spring system is given by T = 2 pi sqrt(m / k) = 2 pi sqrt(ml / YA).

Multiple choice physics measurements and units measuring mass measurement of mass measuring instruments

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:

  1. 15 kg

  2. 22 kg

  3. 50 kg

  4. 0.5 kg
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to the question,

The maximum mass scale can read $M=50\,kg$
The maximum displcement of spring $=$ 
length of scale, $l=20\,cm\,=0.2\,m$
$T$ (time period) $=0.6\,s$
Maximum force exerted on the spring $F=mg$
So,
$g=$acceleration due to gravity $ = 9.8\,m/{s^2}$
$F = 50 \times 9.8 = 490$
Since, speing constant,
$k = \frac{F}{l}$
$ = \frac{{490}}{{0.2}}$
$ = 2450\,N\,{m^{ - 1}}$
$m$ is suspended from the balance 
$T = 2\pi \sqrt {\frac{m}{k}} $
Since,
$m = {\left( {\frac{T}{{2\pi }}} \right)^2} \times k$
$ = {\left( {\frac{{0.6}}{{2 \times 3.14}}} \right)^2} \times 2450$
$ \approx 22\,kg$

Multiple choice physics measurements and units measuring mass measurement of mass measuring instruments

A spring balance reads $10kg$ when a bucket of water is suspended from it. What is the reading on the spring balance when an ice cube of mass $1.5kg$ is into the bucket

  1. 22.5 kg

  2. 2.25 kg

  3. 1.15 kg

  4. 11.5 kg
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A spring balance measures the total weight of the system. Adding an ice cube increases the total weight by the weight of the ice cube (1.5 kg). Thus, 10 kg + 1.5 kg = 11.5 kg.

Multiple choice physics measurements and units measuring mass measurement of mass measuring instruments

A $20 N$ metal block is suspended by a spring balance. A beaker containing some water is placed on a weighing machine which reads $40 N$. The spring balance is now lowered so that the block gets immersed in the water. The spring balance now reads $16 N$4. The reading of the weighing machine will be -  

  1. $36 N$
  2. $60 N$
  3. $44 N$
  4. $56 N$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The block loses 20 N - 16 N = 4 N of weight due to buoyancy. By Newton's third law, the water exerts an upward force of 4 N on the block, and the block exerts a downward force of 4 N on the water. The weighing machine reading increases by 4 N: 40 N + 4 N = 44 N.

Multiple choice physics measurements and units measuring mass measurement of mass measuring instruments

A body of mass 2 kg is hung on a spring balance mounted vertically in a lift. If the lift descends with an acceleration equal to the acceleration due to gravity g the reading of the spring balance will be

  1. 4 kg

  2. 2 X g kg

  3. 2/g kg

  4. zero
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The apparent weight in a vertical lift is given by W = m(g - a). When the lift descends with an acceleration equal to g, the downward acceleration equals the acceleration due to gravity, resulting in apparent weightlessness where W = m(g - g) = 0.

Multiple choice physics measurements and units measuring mass measurement of mass measuring instruments

The weight of a balloon is $W _1$ when empty and $W _2$ when filled with air. Both are weighed in air by the same sensitive spring balance and under identical condition. Then

  1. $W _1=W _2$, as the weight of air in the balloon is offset by the force of buoyancy on it
  2. $W _2 < W _1$, due to the force of buoyancy acting on the filled balloon
  3. $W _2 > W _1$ as the air inside is of a greater pressure and hence has greater density than the air outside
  4. $W _2=W _1+$ weight of the air inside it
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When the balloon is filled with air at higher pressure, the density of the air inside is greater than the density of the air outside, making the filled balloon heavier.

Multiple choice physics measurements and units measuring mass measurement of mass measuring instruments

What principle is used In a  newton spring balance?

  1. The mass of an object depends on its density.

  2. The mass of an object depends an the gravity pulling

  3. The weight of an object is directly proportional to its mass.

  4. The extension of the spring is directly proportional to the force pulling it.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A spring balance operates on Hooke's Law, which states that the extension of a spring is directly proportional to the force applied to it.

Multiple choice physics measurements and units measuring mass measurement of mass measuring instruments

A body is attached to a spring balance suspended from a stand. The reading on the balance is $0.5$kg. The two together are detached from the stand and allowed to fall through a height. While falling the reading in the balance will be.

  1. More than $0.5$ kg depending on the height
  2. Less than $0.5$ kg but not zero

  3. Zero
  4. $0.5$ kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When the spring balance and the body fall together, they are in a state of free fall. In this state, both the body and the spring balance experience the same acceleration due to gravity, meaning there is no net force exerted by the body on the spring. Consequently, the reading on the balance becomes zero.