Answer
Verified
89.7k+ views
Hint: Solve the given equation and check for each option one by one.
Use the formula, velocity in S.H.M$v = w\sqrt {{A^2} - {x^2}} $.
Complete step by step solution:
Given: ${v^2} = 144 - 9{x^2}$
$v = \sqrt {144 - 9{x^2}}$
$\Rightarrow \sqrt {9(16 - {x^2})}$
$\Rightarrow 3\sqrt {16 - {x^2}} ....(1) $
Comparing it with the velocity in S.H.M
$v = \omega \sqrt {{A^2} - {x^2}} $
We get,
$\omega = 3$
${A^2} = 16$
$\Rightarrow A = 4m$
In S.H.M, $displacement < distance$ hence (A) is correct.
Now, $a = - \omega {x^2}$
At $x = 3, \omega = 3$
$a = - {(3)^2}(3)$
$a = - 27m/{s^2}$
$\left| a \right| = 27m/{s^2} $
Hence, (B) is also correct.
Now,
$T = {{2\pi } \over \omega}$
Putting value of $ \omega = 3$
$T = {{2\pi } \over 3}$
Hence, (C) is also correct.
The maximum displacement is amplitude = $4unit$
Hence, (D) is also correct.
Hence, all the above are correct.
Note: While solving this type question we should have a clear understanding of the entire concept so that we can apply one into the other and deduce fruitful results.
Use the formula, velocity in S.H.M$v = w\sqrt {{A^2} - {x^2}} $.
Complete step by step solution:
Given: ${v^2} = 144 - 9{x^2}$
$v = \sqrt {144 - 9{x^2}}$
$\Rightarrow \sqrt {9(16 - {x^2})}$
$\Rightarrow 3\sqrt {16 - {x^2}} ....(1) $
Comparing it with the velocity in S.H.M
$v = \omega \sqrt {{A^2} - {x^2}} $
We get,
$\omega = 3$
${A^2} = 16$
$\Rightarrow A = 4m$
In S.H.M, $displacement < distance$ hence (A) is correct.
Now, $a = - \omega {x^2}$
At $x = 3, \omega = 3$
$a = - {(3)^2}(3)$
$a = - 27m/{s^2}$
$\left| a \right| = 27m/{s^2} $
Hence, (B) is also correct.
Now,
$T = {{2\pi } \over \omega}$
Putting value of $ \omega = 3$
$T = {{2\pi } \over 3}$
Hence, (C) is also correct.
The maximum displacement is amplitude = $4unit$
Hence, (D) is also correct.
Hence, all the above are correct.
Note: While solving this type question we should have a clear understanding of the entire concept so that we can apply one into the other and deduce fruitful results.
Recently Updated Pages
Name the scale on which the destructive energy of an class 11 physics JEE_Main
Write an article on the need and importance of sports class 10 english JEE_Main
Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main
Choose the one which best expresses the meaning of class 9 english JEE_Main
What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main
A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main