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Physics-

General

Easy

Question

A small block is connected to one end of a massless spring of un-stretched length $4.9 m$ . The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by $0.2 m$ and released from rest at $t equals 0.$ It then executes simple harmonic motion with angular frequency $omega equals fraction numerator pi over denominator 3 end fraction r a d divided by s.$ Simultaneously at $t equals 0 comma$ a small pebble is projected with speed $v$ frompoint $P$ is at angle of $45 degree$ as shown in the figure. Point $P$ is at a horizontal distance of $10 blank m$ from $O.$ If the pebble hits the block at $t equals 1 s comma$ the value of $v$ is (take $g equals 10 m divided by s to the power of 2 end exponent$ )

$\sqrt{50} m / s$
$\sqrt{51} m / s$
$\sqrt{52} m / s$
$\sqrt{53} m / s$

The correct answer is: $square root of 50 m divided by s$

The block is released from $A$
$x equals 4.9 m plus open parentheses 0.2 m close parentheses sin invisible function application open parentheses omega t plus fraction numerator pi over denominator 2 end fraction close parentheses$
at $t equals 1 s semicolon x equals 5 m$
so range of projectile will be $5 m$
Now $5 equals fraction numerator v to the power of 2 end exponent sin invisible function application 90 degree over denominator g end fraction rightwards double arrow v to the power of 2 end exponent equals 50 rightwards double arrow v equals square root of 50$

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