The potential energy function for a particle executing linear SHM is given by V(x)= kx where k is the force constant of the oscillator. For k = 0.5N/m, the graph of V(x) versus x is shown in the figure. A particle of total energy E turns back when it reaches x x = ± m . If V and K indicate the P.E. and K.E., respectively of the particle at x = +xm, then which of the following is correct?
This is a multiple choice answer as classified in NCERT Exemplar
(b) Total energy is E=KE+PE……………1
When particle is at x =xm i.e at extreme position, returns back. Hence at x=xm and x=0 KE=0
From eqn1
E= PE+0 = PE= V (xm)=1/2kxm2
<p><span data-teams="true">This is a multiple choice answer as classified in NCERT Exemplar</span></p><p> (b) Total energy is E=KE+PE……………1</p><p>When particle is at x =x<sub>m</sub> i.e at extreme position, returns back. Hence at x=x<sub>m</sub> and x=0 KE=0</p><p>From eqn1</p><p>E= PE+0 = PE= V (x<sub>m</sub>)=1/2kx<sub>m</sub><sup>2</sup></p>
This is a multiple choice answer as classified in NCERT Exemplar
(b) conserving energy between “O” ans ”A”
Ui + Ki = Uf + Kf
0+1/2mv2= mgh + 1/2mv’
(v’)2=v2-2gh = v’= ……….1
Let speed after emerging be v1 then
=1/2mv12=1/2[1/2mv’2]
1/2m(v1)2=1/4m(v’)2=1/4m[v2-2gh]
V1=………….2
From eqn 1 and 2
So v1 = v’/=v2(v’/2)
v1>v’/2
hence after emerging from the target velocity of the bullet is more than half of its earlier velocity v’
(d) as the velocity of the bullet changes to v’ which is less than v’ hence , path
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This is a multiple choice answer as classified in NCERT Exemplar
(b) conserving energy between “O” ans ”A”
Ui + Ki = Uf + Kf
0+1/2mv2= mgh + 1/2mv’
(v’)2=v2-2gh = v’= ……….1
Let speed after emerging be v1 then
=1/2mv12=1/2[1/2mv’2]
1/2m(v1)2=1/4m(v’)2=1/4m[v2-2gh]
V1=………….2
From eqn 1 and 2
So v1 = v’/=v2(v’/2)
v1>v’/2
hence after emerging from the target velocity of the bullet is more than half of its earlier velocity v’
(d) as the velocity of the bullet changes to v’ which is less than v’ hence , path, followed will change and the bullet reaches at point B instead of A
(f) as the bullet is passing through the target the loss in energy of the bullet is transferred to particles of the target . therefore their internal energy increases.
This is a multiple choice answer as classified in NCERT Exemplar
(b, d) When a man of mass m climbs up the staircases of height L, work done by the gravitational force on the man is mgl work done by internal muscular forces will be mgL as the change in kinetic is almost zero.
Hence total work done =-mgL + mgL=0
As the point of application of the contact forces does not move hence work done by reaction forces will be zero.
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