2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main - Mock Test - 14

  • question_answer
    In a particular system, the unit of length, mass and time are chosen to be 10 cm, 10 g and 0.1 s respectively. The unit of force in this system will be equivalent to

    A) 0.1 N     

    B) 1 N

    C) 10 N          

    D) 100 N

    Correct Answer: A

    Solution :

    [a]:
    \[{{M}_{1}}=10g\] \[{{M}_{2}}=1kg\]
    \[{{L}_{1}}=10cm\] \[{{L}_{2}}=1m\]
    \[{{T}_{1}}=0.1s\] \[{{T}_{2}}=1s\]
    \[{{n}_{1}}=1\] \[{{n}_{2}}=?\]
    The dimensional formula of force is \[[ML{{T}^{-2}}]\]. \[\therefore \]\[a=1,b=1,c=-2\] \[{{n}_{2}}={{n}_{1}}{{\left( \frac{{{M}_{1}}}{{{M}_{2}}} \right)}^{a}}{{\left( \frac{{{L}_{1}}}{{{L}_{2}}} \right)}^{b}}{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{c}}\] \[=1{{\left( \frac{10g}{1kg} \right)}^{1}}{{\left( \frac{10cm}{1m} \right)}^{1}}{{\left( \frac{0.1s}{1s} \right)}^{-2}}\] \[=1{{\left( \frac{{{10}^{-2}}kg}{1kg} \right)}^{1}}{{\left( \frac{{{10}^{-1}}m}{1m} \right)}^{1}}{{\left( \frac{0.1s}{1s} \right)}^{-2}}\] \[=\frac{1\times {{10}^{-2}}\times {{10}^{-1}}}{{{10}^{-2}}}={{10}^{-1}}=0.1\] Hence, the unit of force in a given system will equivalent to 0.1 N.               


You need to login to perform this action.
You will be redirected in 3 sec spinner