Tag: physics

Questions Related to physics

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:

physics measurements and units measuring mass measurement of mass measuring instruments

  1. 15 kg

  2. 22 kg

  3. 50 kg

  4. 0.5 kg

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Correct Option: B
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$

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

physics measurements and units measuring mass measurement of mass measuring instruments

  1. 22.5 kg

  2. 2.25 kg

  3. 1.15 kg

  4. 11.5 kg

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Correct Option: D

A child stands on a bathroom scale while riding in an elevator. The child's weight when the elevator is not moving is 100 Ibs. What does the scale read when the elevator accelerates upward while travelling downward?

physics measurements and units measuring mass measurement of mass measuring instruments

  1. greater than 100 Ibs

  2. less than 100 Ibs

  3. exactly 100 Ibs

  4. The same as it reads when accelerating downward while travelling upward, by symmetry.

Show answer
Correct Option: A
Explanation:

Given,

When lift is not moving, gravity force act downward, weighing machine show $\vec{F}=m\vec{g}=100\,lbs\,$force.

When lift start moving upward with acceleration$\vec{a}$, Normal reaction force on child increase by $m\vec{a}$

Therefore, net weight on weighing machine become, $\vec{F}=m\vec{g}+m\vec{a}$

Hence, scale will show weigh greater than $100\,lbs$force.

A body of mass $32 \,kg$ is suspended by a spring balance from the roof of a vertically operating lift and going downward from rest. At the instants the lift has covered $20 \,m$ and $50 \,m$, the spring balance showed $30 \,kg$ and $36 \,kg$ respectively. Then the velocity of the lift is:

physics measurements and units measuring mass measurement of mass measuring instruments

  1. decreasing at $20 \,m$ and increasing at $50 \,m$

  2. increasing at $20 \,m$ and decreasing at $50 \,m$

  3. continuously decreasing at a steady rate throughout the journey

  4. constantly increasing at constant rate throughout the journey.

Show answer
Correct Option: B
Explanation:

According to Fbd

We know that,

$N=m\left( g-a \right)$

So, if $N<mg$

It is a case of downward acceleration

Then, the velocity is increase

Again, if $N>mg$

It is a case of downward retardation

Then, the velocity is decreases

Hence, the velocity is increasing at $20$ m and decreasing at $50\ m$

The two arms of a balance are of unequal length. An object when placed in the left pan of the balance weighs  4kg. The same object when placed in the right pan of the balance weighs 9 kg. The actual (or) true mass of the object is 

physics measurements and units measuring mass measurement of mass measuring instruments

  1. $5.5kg$

  2. $6kg$

  3. $6.5kg$

  4. $7kg$

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Correct Option: C

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 -  

physics measurements and units measuring mass measurement of mass measuring instruments

  1. $36 N$

  2. $60 N$

  3. $44 N$

  4. $56 N$

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Correct Option: C

Two equal masses m and m are hung from a spring balance whose scale pans differ in vertical height by h. If $\rho$ is the mean density of earth ,then what is the error in weighing?

physics measurements and units measuring mass measurement of mass measuring instruments

  1. $\frac { 8 } { 3 } \pi \mathrm { G\rho m h }$

  2. $\frac { 4 } { 3 } \pi \mathrm { G\rho m h }$

  3. $\frac { 5 } { 3 } \pi \mathrm { G\rho m h }$

  4. $\infty$

Show answer
Correct Option: A

A boy whose mass is $50$ kg stands on spring balance inside a lift. The lift starts to ascend with an acceleration of $2{ m/s }^{ -2 }$. The reading of the machine or balance (g = 10${ m/s }^{ -2 }$) is

physics measurements and units measuring mass measurement of mass measuring instruments

  1. 50 kg

  2. zero

  3. 49 kg

  4. 60 kg

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Correct Option: D

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

physics measurements and units measuring mass measurement of mass measuring instruments

  1. 4 kg

  2. 2 X g kg

  3. 2/g kg

  4. zero

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Correct Option: A

A bird is sitting in a wire cage hanging form the spring balance. Let the reading of the spring balance be $W _1$. If the bird flies about inside the cage, the reading of the spring balance is $W _2$. Which of the following is true :-

physics measurements and units measuring mass measurement of mass measuring instruments

  1. $W _1=W _2$

  2. $W _1>W _2$

  3. $W _1 < W _2$

  4. Nothing definite can be pridicted

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Correct Option: B