UPSEE Solved Model Paper 2

Let x be the compression of spring. The kinetic energy of the clock (=

1

2

mv2) is used
(i) imparting potential energy = (=

1

2

kx2) to the spring ands
(ii) doing work (= fx) against friction. Thus

1

2

mv2 =

1

2

kx2+fx

1

2

×2×(4)2 =

1

2

×10000×x2+15x
⇒ 5000x2+15x−16 = 0
The two roots are
x =

−15±[(15)2+4×5000×16] 1 2

2×5000

=

−15±(225+320000) 1 2

10000

=

−15±556

10000

= 0.0551 m and - 0.0581 m
Since negative value of x is not permissible, x = 0.0551 m = 5.51 cm.