Motion in a Plane: JEE Mains Previous Year Questions (2021-2024) | Physics for JEE Main & Advanced PDF Download

 Page 1


 
2024 
 
Q1 - 2024 (01 Feb Shift 1) 
A particle moving in a circle of radius ?? with uniform speed takes time T to complete one 
revolution. If this particle is projected with the same speed at an angle ?? to the 
horizontal, the maximum height attained by it is equal to 4R. The angle of projection ?? is 
then given by : 
(1) sin
-1
 
2?? ?? 2
?? 2
?? 
1
2
 
(2) sin
-1
 
?? 2
R
2gT
2
 
1
2
 
(3) cos
-1
 
2gT
2
?? 2
R
 
1
2
 
(4) cos
-1
 
?? R
2gT
2
 
1
2
 
Q2 - 2024 (29 Jan Shift 1) 
If the radius of curvature of the path of two particles of same mass are in the ratio 3:4, 
then in order to have constant centripetal force, their velocities will be in the ratio of: 
(1)  3:2 
(2) 1: 3 
(3)  3:1 
(4) 2: 3 
Q3 - 2024 (29 Jan Shift 1) 
A ball rolls off the top of a stairway with horizontal velocity ?? . The steps are 0.1m high 
and 0.1m wide. The minimum velocity u with which that ball just hits the step 5 of the 
stairway will be  xms
-1
 where x = [use 
 
g = 10m/s
2
 . 
Q4 - 2024 (30 Jan Shift 1) 
Page 2


 
2024 
 
Q1 - 2024 (01 Feb Shift 1) 
A particle moving in a circle of radius ?? with uniform speed takes time T to complete one 
revolution. If this particle is projected with the same speed at an angle ?? to the 
horizontal, the maximum height attained by it is equal to 4R. The angle of projection ?? is 
then given by : 
(1) sin
-1
 
2?? ?? 2
?? 2
?? 
1
2
 
(2) sin
-1
 
?? 2
R
2gT
2
 
1
2
 
(3) cos
-1
 
2gT
2
?? 2
R
 
1
2
 
(4) cos
-1
 
?? R
2gT
2
 
1
2
 
Q2 - 2024 (29 Jan Shift 1) 
If the radius of curvature of the path of two particles of same mass are in the ratio 3:4, 
then in order to have constant centripetal force, their velocities will be in the ratio of: 
(1)  3:2 
(2) 1: 3 
(3)  3:1 
(4) 2: 3 
Q3 - 2024 (29 Jan Shift 1) 
A ball rolls off the top of a stairway with horizontal velocity ?? . The steps are 0.1m high 
and 0.1m wide. The minimum velocity u with which that ball just hits the step 5 of the 
stairway will be  xms
-1
 where x = [use 
 
g = 10m/s
2
 . 
Q4 - 2024 (30 Jan Shift 1) 
A particle of mass ?? projected with a velocity ' ?? ' making an angle of 30
°
 with the 
horizontal. The magnitude of angular momentum of the projectile about the point of 
projection when the particle is at its maximum height his : 
(1) 
 3
16
?? ?? 3
?? 
(2) 
 3
2
?? ?? 2
?? 
(3) 
?? ?? 3
 2?? 
(4) zero 
Q5 - 2024 (30 Jan Shift 2) 
Projectiles A and B are thrown at angles of 45
°
 and 60
°
 with vertical respectively from 
top of a 400m high tower. If their ranges and times of flight are same, the ratio of their 
speeds of projection ?? ?? :?? ?? is : 
[We changed options. In official NTA paper no option was correct.] 
(1) 1: 3 
(2)  2:1 
(3) 1:2 
(4) 1:1 
Q6 - 2024 (31 Jan Shift 1) 
A body starts falling freely from height H hits an inclined plane in its path at height h. As 
a result of this perfectly elastic impact, the direction of the velocity of the body becomes 
horizontal. The value of 
?? h
 for which the body will take the maximum time to reach the 
ground is 
Answer Key 
Q1 (1)  
Q2 (1)  
Q3 (2)  
Q4 (1) 
Q5 (4) 
Q6 (2) 
Solutions 
Q1 
2?? R
T
= V 
Page 3


 
2024 
 
Q1 - 2024 (01 Feb Shift 1) 
A particle moving in a circle of radius ?? with uniform speed takes time T to complete one 
revolution. If this particle is projected with the same speed at an angle ?? to the 
horizontal, the maximum height attained by it is equal to 4R. The angle of projection ?? is 
then given by : 
(1) sin
-1
 
2?? ?? 2
?? 2
?? 
1
2
 
(2) sin
-1
 
?? 2
R
2gT
2
 
1
2
 
(3) cos
-1
 
2gT
2
?? 2
R
 
1
2
 
(4) cos
-1
 
?? R
2gT
2
 
1
2
 
Q2 - 2024 (29 Jan Shift 1) 
If the radius of curvature of the path of two particles of same mass are in the ratio 3:4, 
then in order to have constant centripetal force, their velocities will be in the ratio of: 
(1)  3:2 
(2) 1: 3 
(3)  3:1 
(4) 2: 3 
Q3 - 2024 (29 Jan Shift 1) 
A ball rolls off the top of a stairway with horizontal velocity ?? . The steps are 0.1m high 
and 0.1m wide. The minimum velocity u with which that ball just hits the step 5 of the 
stairway will be  xms
-1
 where x = [use 
 
g = 10m/s
2
 . 
Q4 - 2024 (30 Jan Shift 1) 
A particle of mass ?? projected with a velocity ' ?? ' making an angle of 30
°
 with the 
horizontal. The magnitude of angular momentum of the projectile about the point of 
projection when the particle is at its maximum height his : 
(1) 
 3
16
?? ?? 3
?? 
(2) 
 3
2
?? ?? 2
?? 
(3) 
?? ?? 3
 2?? 
(4) zero 
Q5 - 2024 (30 Jan Shift 2) 
Projectiles A and B are thrown at angles of 45
°
 and 60
°
 with vertical respectively from 
top of a 400m high tower. If their ranges and times of flight are same, the ratio of their 
speeds of projection ?? ?? :?? ?? is : 
[We changed options. In official NTA paper no option was correct.] 
(1) 1: 3 
(2)  2:1 
(3) 1:2 
(4) 1:1 
Q6 - 2024 (31 Jan Shift 1) 
A body starts falling freely from height H hits an inclined plane in its path at height h. As 
a result of this perfectly elastic impact, the direction of the velocity of the body becomes 
horizontal. The value of 
?? h
 for which the body will take the maximum time to reach the 
ground is 
Answer Key 
Q1 (1)  
Q2 (1)  
Q3 (2)  
Q4 (1) 
Q5 (4) 
Q6 (2) 
Solutions 
Q1 
2?? R
T
= V 
Maximum height H =
v
2
sin
2
? ?? 2g
 
4R =
4?? 2
R
2
T
2
2g
sin
2
? ?? 
sin? ?? =
 
2gT
2
?? 2
R
 
?? = sin
-1
? 
2gT
2
?? 2
R
 
1
2
 
Q2 
Given m
1
= m
2
 and 
?? 1
?? 2
=
3
4
 
As centripetal force ?? =
?? 2
?? 
In order to have constant (same in this question) centripetal force 
F
1
= F
2
 
m
1
v
1
2
r
1
=
m
2
v
2
2
r
2
 
?
v
1
v
2
= 
r
1
r
2
=
 3
2
 
Q3 
 
Page 4


 
2024 
 
Q1 - 2024 (01 Feb Shift 1) 
A particle moving in a circle of radius ?? with uniform speed takes time T to complete one 
revolution. If this particle is projected with the same speed at an angle ?? to the 
horizontal, the maximum height attained by it is equal to 4R. The angle of projection ?? is 
then given by : 
(1) sin
-1
 
2?? ?? 2
?? 2
?? 
1
2
 
(2) sin
-1
 
?? 2
R
2gT
2
 
1
2
 
(3) cos
-1
 
2gT
2
?? 2
R
 
1
2
 
(4) cos
-1
 
?? R
2gT
2
 
1
2
 
Q2 - 2024 (29 Jan Shift 1) 
If the radius of curvature of the path of two particles of same mass are in the ratio 3:4, 
then in order to have constant centripetal force, their velocities will be in the ratio of: 
(1)  3:2 
(2) 1: 3 
(3)  3:1 
(4) 2: 3 
Q3 - 2024 (29 Jan Shift 1) 
A ball rolls off the top of a stairway with horizontal velocity ?? . The steps are 0.1m high 
and 0.1m wide. The minimum velocity u with which that ball just hits the step 5 of the 
stairway will be  xms
-1
 where x = [use 
 
g = 10m/s
2
 . 
Q4 - 2024 (30 Jan Shift 1) 
A particle of mass ?? projected with a velocity ' ?? ' making an angle of 30
°
 with the 
horizontal. The magnitude of angular momentum of the projectile about the point of 
projection when the particle is at its maximum height his : 
(1) 
 3
16
?? ?? 3
?? 
(2) 
 3
2
?? ?? 2
?? 
(3) 
?? ?? 3
 2?? 
(4) zero 
Q5 - 2024 (30 Jan Shift 2) 
Projectiles A and B are thrown at angles of 45
°
 and 60
°
 with vertical respectively from 
top of a 400m high tower. If their ranges and times of flight are same, the ratio of their 
speeds of projection ?? ?? :?? ?? is : 
[We changed options. In official NTA paper no option was correct.] 
(1) 1: 3 
(2)  2:1 
(3) 1:2 
(4) 1:1 
Q6 - 2024 (31 Jan Shift 1) 
A body starts falling freely from height H hits an inclined plane in its path at height h. As 
a result of this perfectly elastic impact, the direction of the velocity of the body becomes 
horizontal. The value of 
?? h
 for which the body will take the maximum time to reach the 
ground is 
Answer Key 
Q1 (1)  
Q2 (1)  
Q3 (2)  
Q4 (1) 
Q5 (4) 
Q6 (2) 
Solutions 
Q1 
2?? R
T
= V 
Maximum height H =
v
2
sin
2
? ?? 2g
 
4R =
4?? 2
R
2
T
2
2g
sin
2
? ?? 
sin? ?? =
 
2gT
2
?? 2
R
 
?? = sin
-1
? 
2gT
2
?? 2
R
 
1
2
 
Q2 
Given m
1
= m
2
 and 
?? 1
?? 2
=
3
4
 
As centripetal force ?? =
?? 2
?? 
In order to have constant (same in this question) centripetal force 
F
1
= F
2
 
m
1
v
1
2
r
1
=
m
2
v
2
2
r
2
 
?
v
1
v
2
= 
r
1
r
2
=
 3
2
 
Q3 
 
The ball needs to just cross 4 steps to just hit 5
th 
 step 
Therefore, horizontal range (R)= 0.4m 
R = u.t 
Similarly, in vertical direction 
h =
1
2
gt
2
 
0.4 =
1
2
gt
2
 
0.4 =
1
2
g 
0.4
u
 
2
 
u
2
= 2 
u = 2m/s 
Therefore, ?? = 2 
Q4 
L =?? ?? cos? ?? ?? 
=?? ?? cos? ?? ×
?? 2
sin
2
? ?? 2?? 
=
?? ?? 3
2?? ×
 3
2
× 
1
2
 
2
=
 3?? ?? 3
16?? 
Q5 
Page 5


 
2024 
 
Q1 - 2024 (01 Feb Shift 1) 
A particle moving in a circle of radius ?? with uniform speed takes time T to complete one 
revolution. If this particle is projected with the same speed at an angle ?? to the 
horizontal, the maximum height attained by it is equal to 4R. The angle of projection ?? is 
then given by : 
(1) sin
-1
 
2?? ?? 2
?? 2
?? 
1
2
 
(2) sin
-1
 
?? 2
R
2gT
2
 
1
2
 
(3) cos
-1
 
2gT
2
?? 2
R
 
1
2
 
(4) cos
-1
 
?? R
2gT
2
 
1
2
 
Q2 - 2024 (29 Jan Shift 1) 
If the radius of curvature of the path of two particles of same mass are in the ratio 3:4, 
then in order to have constant centripetal force, their velocities will be in the ratio of: 
(1)  3:2 
(2) 1: 3 
(3)  3:1 
(4) 2: 3 
Q3 - 2024 (29 Jan Shift 1) 
A ball rolls off the top of a stairway with horizontal velocity ?? . The steps are 0.1m high 
and 0.1m wide. The minimum velocity u with which that ball just hits the step 5 of the 
stairway will be  xms
-1
 where x = [use 
 
g = 10m/s
2
 . 
Q4 - 2024 (30 Jan Shift 1) 
A particle of mass ?? projected with a velocity ' ?? ' making an angle of 30
°
 with the 
horizontal. The magnitude of angular momentum of the projectile about the point of 
projection when the particle is at its maximum height his : 
(1) 
 3
16
?? ?? 3
?? 
(2) 
 3
2
?? ?? 2
?? 
(3) 
?? ?? 3
 2?? 
(4) zero 
Q5 - 2024 (30 Jan Shift 2) 
Projectiles A and B are thrown at angles of 45
°
 and 60
°
 with vertical respectively from 
top of a 400m high tower. If their ranges and times of flight are same, the ratio of their 
speeds of projection ?? ?? :?? ?? is : 
[We changed options. In official NTA paper no option was correct.] 
(1) 1: 3 
(2)  2:1 
(3) 1:2 
(4) 1:1 
Q6 - 2024 (31 Jan Shift 1) 
A body starts falling freely from height H hits an inclined plane in its path at height h. As 
a result of this perfectly elastic impact, the direction of the velocity of the body becomes 
horizontal. The value of 
?? h
 for which the body will take the maximum time to reach the 
ground is 
Answer Key 
Q1 (1)  
Q2 (1)  
Q3 (2)  
Q4 (1) 
Q5 (4) 
Q6 (2) 
Solutions 
Q1 
2?? R
T
= V 
Maximum height H =
v
2
sin
2
? ?? 2g
 
4R =
4?? 2
R
2
T
2
2g
sin
2
? ?? 
sin? ?? =
 
2gT
2
?? 2
R
 
?? = sin
-1
? 
2gT
2
?? 2
R
 
1
2
 
Q2 
Given m
1
= m
2
 and 
?? 1
?? 2
=
3
4
 
As centripetal force ?? =
?? 2
?? 
In order to have constant (same in this question) centripetal force 
F
1
= F
2
 
m
1
v
1
2
r
1
=
m
2
v
2
2
r
2
 
?
v
1
v
2
= 
r
1
r
2
=
 3
2
 
Q3 
 
The ball needs to just cross 4 steps to just hit 5
th 
 step 
Therefore, horizontal range (R)= 0.4m 
R = u.t 
Similarly, in vertical direction 
h =
1
2
gt
2
 
0.4 =
1
2
gt
2
 
0.4 =
1
2
g 
0.4
u
 
2
 
u
2
= 2 
u = 2m/s 
Therefore, ?? = 2 
Q4 
L =?? ?? cos? ?? ?? 
=?? ?? cos? ?? ×
?? 2
sin
2
? ?? 2?? 
=
?? ?? 3
2?? ×
 3
2
× 
1
2
 
2
=
 3?? ?? 3
16?? 
Q5 
 
For u
A
&u
B
 time of flight and range can not be same. So above options are incorrect. 
Q6 
 
Total time of flight = T