Question

figure shows a smooth horizontal track ,a part of which is a vertical circle of radius 1.0 m . a block of mass 0.1 kg is pushed against a spring of spring constant 300 N/m fixed at one end.the initial compression of the spring so that the block presses the track with the force of 1.0 N when reach the point p

a. 0.1 m
b. 0.2 m
c. 0.3 m
d. 0.4 m

plz give answer from the option only plz..​

Answer 1

Answer:

Ans is a. 0.1

PLEASE MARK ME BRIGHTEST

Answer 2

Answer:

b. 0.1m

compression required in the spring is 0.1m.

Explanation:

At point P, block and track apply equal force on each other,

Therefore, $\frac{Mv^2}{R} = 1N$

where, $M$=mass of object = 0.1kg

$v=$velocity

$R$=radius o circular track=1m

$\implies v^2=\frac{R}{M} = \frac{1}{0.1} = 10$

Energy provided by spring to the mass = $\frac{1}{2} Kx^2$

where, $K$=spring constant

$x$=extension in spring

Energy of the block at P = K.E. + P.E = $\frac{1}{2} Mv^2 + MgR$

As energy is conserved, equating,

 $\implies\frac{1}{2} Kx^2 = \frac{1}{2} Mv^2 + MgR$

$\implies\frac{1}{2}*300*x^2 = \frac{1}{2}*0.1*10 + 0.1*10*1$

$\implies150*x^2 = 0.5 + 1$

$\implies x^2 = \frac{1.5}{150}=0.01$

$\implies x=0.1m$

compression required in the spring is 0.1m.

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