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Two blocks A and B of masses m and 2m, respectively, are connected by a massless spring of spring constant K. This system lies over a smooth horizontal surface. At t = 0, block A has velocity u towards right as shown, while the speed of block B is zero, and the length of the spring is equal to its natural length at that instant. In each situation column I, certain statements are given and corresponding results are given in column II. Match the statements in column I with the corresponding results in column II.
Column I Column II
i The velocity of block A a Can never be zero
ii The velocity of block B b May be zero at certain instants of time
iii The kinetic energy of the system of two blocks c Is minimum at maximum compression of spring
iv The potential energy of spring d is maximum at maximum extension of spring

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(i) a (ii) b (iii) a, c (iv) b,d

(i) a (ii) b (iii) c (iv) d

(i) a, b (ii) b, c (iii) b (iv) a

(i) c, d (ii) d (iii) b,c (iv) b

answer is A.

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Detailed Solution

(i) If velocity of bock A is zero, from conversation of momentum, speed of block B is 2u. Then KE of block $B = \frac{1}{2} m {(2 u)}^{2} = 2 m u^{2}$ is greater then net mechanical energy of the system. Since this is not possible, velocity of A can never be zero.

(ii) Since initial velocity of B is zero, it shall b zero for many other instant of time.

(iii) Since momentum of system is non-zero, KE of system cannot be zero. Also KE of system is minimum at maximum extension of the spring.

(iv) The potential energy of spring shall be zero whenever it comes to natural length, Also PE of spring is maximum at maximum extension of the spring.

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