A solid sphere, a thinwalled hollow sphere, a solid cylinder, a thinwalled hollow cylinder and a ring, each of mass and radius , are simultaneously released at rest from the top of an inclined plane, as shown in Figure. The objects roll down the plane without slipping. Also we may consider the objects and the surface on which they roll to be perfectly rigid. Match Columns I and II
ColumnI 
Column II 

(A) 
Time taken to reach the bottom is maximum for 
(p) 
Solid sphere 

(B) 
Angular acceleration is maximum for 
(q) 
Hollow cylinder 

(C) 
Kinetic energy at the bottom is the same for 
(r) 
Hollow sphere 

(D) 
Rotational kinetic energy is maximum for 
(s) 
Ring 

CODES : 


A 
B 
C 
D 



a) 
B,d 
a 
a,b,c,d 
b,d 



b) 
b 
d 
c 
a 



c) 
c,d 
b,a 
d 
a 



d) 
c,a 
b,d 
a,c 
a,b,c 


A solid sphere, a thinwalled hollow sphere, a solid cylinder, a thinwalled hollow cylinder and a ring, each of mass and radius , are simultaneously released at rest from the top of an inclined plane, as shown in Figure. The objects roll down the plane without slipping. Also we may consider the objects and the surface on which they roll to be perfectly rigid. Match Columns I and II
ColumnI 
Column II 

(A) 
Time taken to reach the bottom is maximum for 
(p) 
Solid sphere 

(B) 
Angular acceleration is maximum for 
(q) 
Hollow cylinder 

(C) 
Kinetic energy at the bottom is the same for 
(r) 
Hollow sphere 

(D) 
Rotational kinetic energy is maximum for 
(s) 
Ring 

CODES : 


A 
B 
C 
D 



a) 
B,d 
a 
a,b,c,d 
b,d 



b) 
b 
d 
c 
a 



c) 
c,d 
b,a 
d 
a 



d) 
c,a 
b,d 
a,c 
a,b,c 


(a)
But as in rolling,
Solving for acceleration, we have
and time taken