CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

A gun fires a shell and recoils horizontally. If the shell travels with speed v with respect to the barrel, the ratio of speed with which the gun recoils if (i) the barrel is horizontal (ii) inclined at an angle of 30 with horizontal is

A
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
23
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
32
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 23
Let mass of gun is M and that of shell is m. The two cases are shown in the figure as below.

Here v1 and v2 are the recoil speeds of the gun in two cases. As there are no net external forces in horizontal direction, therefore using conservation of linear momentum in horizontal direction in both cases:
For case 1
m(vv1)=Mv1
v1=mvM+m ...(i)
For case 2
From F.B.D, horizontal velocity of shell w.r.t gun is vcos30
Applying PCLM,
m(vcos30v2)=Mv2
v2=3mv2(M+m) ...(ii)
From equations (i) and (ii),
v1v2=23

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Conservation of Momentum
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon