Tag: measurements and units

Questions Related to measurements and units

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.

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

A false balance is such that the beam remains horizontal when the pans are empty. An object weighs ${ w } _{ 1 }$ when placed in one pan and ${ w } _{ 2 }$ when placed in the other pan. Then the weight W of the object is

  1. $\sqrt { { w } _{ 1 }{ w } _{ 2 } } $
  2. $\dfrac { { w } _{ 1 }+{ w } _{ 2 } }{ 2 } $
  3. $\dfrac { 2 }{ \sqrt { { w } _{ 1 }^{ 2 }+{ w } _{ 2 }^{ 2 } } } $
  4. $\sqrt { \dfrac { { w } _{ 1 }^{ 2 }+{ w } _{ 2 }^{ 2 } }{ 2 } } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a false balance with equal arm lengths but unequal pan weights or other systematic errors, the true weight is the arithmetic mean of the weights obtained in the two pans: W = (w1 + w2) / 2.

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

An object hangs from a spring balance. The balance indicates  $30 { N }$  in air and  $20 { N }$  when the object is submerged-in.water. What does the balance indicate when the object is submerged in a liquid. with a density that is half that of water ?

  1. $20 N$
  2. $25 N$
  3. $30 N$
  4. $35 N$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The buoyant force is proportional to the density of the liquid. In water, the loss is 30 - 20 = 10 N. In a liquid with half the density of water, the buoyant force is half, which is 5 N. The reading is 30 - 5 = 25 N.

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

A man is standing on a weighting machine with a block in his hand. The machine records $W$. When he takes the block upwards with some acceleration the machine records $W _1$. When he takes the block down with some acceleration, the machine records $W _2$. Then choose correct option 

  1. $W _1 = W = W _2$
  2. $W _1 < W < W _2$
  3. $W _2 < W < W _1$
  4. $W _2 = W _1 > W$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When the block is accelerated upward, the man exerts more force on the machine (W1 > W). When accelerated downward, the man exerts less force on the machine (W2 < W). Thus, W2 < W < W1.