Two blocks and of masses and , respectively, are connected by a massless spring of spring constant This system lies over a smooth horizontal surface. At , block has velocity towards right as shown, while the speed of block is zero, and the length of the spring is equal to its natural length at that instant. In each situation of 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
ColumnI 
Column II 

(A) 
The velocity of block 
(p) 
Can never be zero 

(B) 
The velocity of block 
(q) 
May be zero at certain instants of time 

(C) 
The kinetic energy of the system of two blocks 
(r) 
Is minimum at maximum compression of spring 

(D) 
The potential energy of spring 
(s) 
Is maximum at maximum extension of spring 

CODES : 


A 
B 
C 
D 



a) 
A,c 
b,d 
a 
b 



b) 
a 
b 
a,c 
b,d 



c) 
d 
b,d 
b 
a,c 



d) 
a 
a 
b 
b,d 


Two blocks and of masses and , respectively, are connected by a massless spring of spring constant This system lies over a smooth horizontal surface. At , block has velocity towards right as shown, while the speed of block is zero, and the length of the spring is equal to its natural length at that instant. In each situation of 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
ColumnI 
Column II 

(A) 
The velocity of block 
(p) 
Can never be zero 

(B) 
The velocity of block 
(q) 
May be zero at certain instants of time 

(C) 
The kinetic energy of the system of two blocks 
(r) 
Is minimum at maximum compression of spring 

(D) 
The potential energy of spring 
(s) 
Is maximum at maximum extension of spring 

CODES : 


A 
B 
C 
D 



a) 
A,c 
b,d 
a 
b 



b) 
a 
b 
a,c 
b,d 



c) 
d 
b,d 
b 
a,c 



d) 
a 
a 
b 
b,d 


(b)
i. If velocity of block is zero, from conservation of momentum, speed of block is Then KE of block is greater than net mechanical energy of the system. Since this is not possible, velocity of can never be zero
ii. Since initial velocity of is zero, it shall be zero for many other instants 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
Centre of mass of a system is unique point which is very helpful in solving the problems related to the motions of rigid bodies. In columns I and II, some statements regarding centre of mass are given. Match the columns: 
ColumnI 
Column II 

(A) 
In the absence of external forces, the internal forces 
(p) 
Inside the material of the body 

(B) 
Centre of mass of a body can be 
(q) 
May affect the motion of individuals 

(C) 
The kinetic energy of the system of two blocks 
(r) 
Do not affect the motion of centre of mass 

(D) 
Centre of mass of a solid cylinder is 
(s) 
Outside the material of the body 

CODES : 


A 
B 
C 
D 



a) 
B,c 
a,d 
c 
a 



b) 
a,d 
c 
b,c 
a 



c) 
b,c 
a 
a,d 
c 



d) 
c 
b,c 
a,d 
a 


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