Tag: physics

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Questions Related to physics

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 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?

  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.
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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:

  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.
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $50\ m$

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

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 

  1. $5.5kg$
  2. $6kg$
  3. $6.5kg$
  4. $7kg$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a false balance with unequal arm lengths L1 and L2, the true mass M is related to the apparent masses W1 and W2 by the geometric mean formula M = sqrt(W1 * W2). Substituting the given values, M = sqrt(4 * 9) = sqrt(36) = 6 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

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?

  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. $\infty$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The difference in gravitational potential due to the height difference h leads to a weight difference. The formula for the error in weighing due to gravity gradient is (8/3) * pi * G * rho * m * h.

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

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

  1. 50 kg

  2. zero

  3. 49 kg

  4. 60 kg
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The apparent weight in an accelerating lift is W = m(g + a). Here, W = 50 * (10 + 2) = 50 * 12 = 600 N. Converting back to kg-force, the reading is 60 kg.

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.