Tag: measuring mass

Questions Related to measuring mass

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.


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 

  1. $5.5kg$

  2. $6kg$

  3. $6.5kg$

  4. $7kg$


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 -  

  1. $36 N$

  2. $60 N$

  3. $44 N$

  4. $56 N$


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?

  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. $\infty$


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

  1. 50 kg

  2. zero

  3. 49 kg

  4. 60 kg


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

  1. 4 kg

  2. 2 X g kg

  3. 2/g kg

  4. zero


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 :-

  1. $W _1=W _2$

  2. $W _1>W _2$

  3. $W _1 < W _2$

  4. Nothing definite can be pridicted


Correct Option: B

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 } } $


Correct Option: B

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. $35 N$


Correct Option: B

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. $W _2 = W _1 > W$


Correct Option: C