Physics-
General
Easy

Question

There are two forces each of magnitude 10 units. One inclined at an angle of 30degree and the other at an angle of 135degree to the positive direction of x minusaxis. The x and y components of the resultant are respectively.

  1. 1.59stack i with hat on top and 12.07 stack j with hat on top  
  2. 10stack i with hat on top and 10 stack j with hat on top  
  3. 1.59stack i with hat on top  
  4. 15.9stack i with hat on top and 12.07 stack j with hat on top  

The correct answer is: 1.59stack i with hat on top and 12.07 stack j with hat on top


    Here stack A with rightwards arrow on top minus stack O P with rightwards arrow on top equals 10 units along O P
    stack B with rightwards arrow on top minus open parentheses stack O Q with rightwards arrow on top close parentheses equals 10 units along O Q
    therefore blank angle X O P equals 30 degree andblank angle X O Q equals 135 degree
    therefore blank angle Q O X to the power of ´ end exponent equals 180 degree minus 135 degree=45degree

    Resolving stack A with rightwards arrow on top and stack B with rightwards arrow on top into two rectangular components we have A cos 30degree along O X and A sin 30degree along O Y. B cos invisible function application 45 degree along O X ´ blank a n d blank B sin invisible function application 45 degree along O ´.
    Resultant component force along X-axis.
    left parenthesis A blank c o s 30 degree minus B s i n 45 right parenthesis stack i with hat on top
    equals open parentheses 10 cross times square root of 3 divided by 2 minus 10 cross times 1 divided by square root of 2 close parentheses stack i with hat on top equals 1.59 stack i with hat on top
    Resultant component force along Y-axis
    equals left parenthesis A blank s i n 30 degree plus B s i n 45 degree right parenthesis stack j with hat on top
    equals open parentheses 10 cross times 1 divided by 2 plus 10 cross times 1 divided by square root of 2 close parentheses stack j with hat on top equals 12.07 stack j with hat on top

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