Physics

Spring Mass Systems

172 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 sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

A horizontal plank has a rectangular block placed on it. The plank starts oscillating vertically and simple harmonically with an amplitude of 40 cm. The block just loses contact with the plank when the later is momentarily at rest. Then

  1. the period of oscillation is $2\pi /5\ s$

  2. the block weighs double its weight when the plank is at one of the positions of momentary at rest

  3. the block weighs 1.5 times its weight on the plank half way down

  4. the block weighs its true weight on the plank, when the latter moves fast
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A spring of force constant K is first stretched by distance a from its natural length and then future by distance b. The work done in stretching the part b is

  1. $\dfrac{1}{2}$Ka(a-b)
  2. $\dfrac{1}{2}$Ka(a+b)
  3. $\dfrac{1}{2}$Kb(a-b)
  4. $\dfrac{1}{2}$Kb(2a+b)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work done by spring in its natural length$=\cfrac{1}{2} \times k \times x^{2}= \cfrac{1}{2} \times k \times a^{2}$

So, total work$=\cfrac{1}{2}k(a+b)^{2}$
for work done for stretching 'b'
$\cfrac { 1 }{ 2 } \times k\times (a+b)^{ 2 }-\cfrac { 1 }{ 2 } \times k\times a^{ 2 }=\cfrac { 1 }{ 2 } \times k\times b\times (2a+b)$

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
B Correct answer
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

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.