JEE Mains · Physics · STD 11 - Newtons laws of motion
- JEE Mains 2014
- Medium
- MCQ
A body of mass \(5\, kg\) under the action of constant force \(\overrightarrow F = {F_x}\hat i + {F_y}\hat j\) has velocity at \(t\,= 0\, s\) as \(\overrightarrow v = \left( {6\hat i - 2\hat j\,m/s} \right)\) and at \(t\, = 10\,s\) as \(\overrightarrow v = +6\hat j\,m/s\). The force \(\overrightarrow F \) is
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(\left( { - 3\hat i + 4\hat j\,} \right)\,N\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{l}
From\,question,\\
Mass\,of\,body,\,m = 5\,kg\\
Vleocity\,at\,t = 0,\\
u = \,\left( {6\hat i - 2\hat j} \right)\,m/s\\
Velocity\,at\,t = 10s,\\
v = + 6\,\hat j\,m/s\\
Force,\,F = ?
\end{array}\)
From\,question,\\
Mass\,of\,body,\,m = 5\,kg\\
Vleocity\,at\,t = 0,\\
u = \,\left( {6\hat i - 2\hat j} \right)\,m/s\\
Velocity\,at\,t = 10s,\\
v = + 6\,\hat j\,m/s\\
Force,\,F = ?
\end{array}\)
\(\begin{array}{l}
Acceleration,\,a = \frac{{v - u}}{t}\\
= \frac{{6\hat j - \left( {6\hat i - 2\hat j} \right)}}{{10}} = - 3\hat i + 4\hat j\,m/{s^2}\\
Force,\,F = ma\\
= 5 \times \frac{{\left( {3\hat i + 4\hat j} \right)}}{5} = \left( { - 3\hat i + 4\hat j} \right)\,N
\end{array}\)
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