Tag: least count of vernier calliper and screw gauge

A physical quantity $Q$ is released to four observable $x,y,z$ and $t$  by the relation
$Q=\dfrac {x^{2/5}z^{3}}{y\sqrt {t}}$ 
The percentage errors of measurement in $x,y,z$ and $t$ are $2.5\%,2\%,0.5\%$ and $1\%$ receptively. The percentage error in $Q$ will be

A steel tape is calibrated at $20 ^ { \circ } \mathrm { C }$. On a cold day when the temperature is $- 15 ^ { \circ } \mathrm { C }$ percentage error in the tape will be $\left[ \alpha _ { \text { steel } } = 1.2 \times 10 ^ { - 5 \cdot 0 } C ^ { - 1 } \right]$

The random error in the arithmetic mean of 100 observations is x, then random error in the arithmetic mean of 400 observation would be

A  faulty thermometer has its fixed point marked 5${ \circ  } _{ C }$ and 95${ \circ  } _{ C }$. this thermometer reads the temperature of a body as ${ 59 }^{ \circ  }$. The correct temperature on Celsius scale is  

If the error in measurement of momentum of a particle is $10$% and mass is known exactly,the permissible error in the determination of kinetic energy is

Length of a thin cylinder as measured by vernier callipers having least cound $0.01\ cm$ is $3.25\ cm$ and its radius of cross-section is measured by a screw gauge having least count $0.01\ mm$ as $2.75\ mm$. The percentage error in the measurement of volume of the cylinder will be

If the error in the measurement of radius of a sphere is 1%, then the error in the measurement of volume will be :

The speed of a body is measured with a positive error of 30%. If the mass of the body is known exactly, the kinetic energy is calculated with an error of

While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. His per-centre error in the n=measurement of g by the relation $g={ 4\pi  }^{ 2 }\left( I/T^{ 2 } \right) $ will be