PREVIOUS EAMCET QUESTIONS

Size: px

Start display at page:

Download "PREVIOUS EAMCET QUESTIONS"

Ferdinand Casey
5 years ago
Views:

1 CENTRE OF MASS PREVIOUS EAMCET QUESTIONS ENGINEERING Two prticles A nd B initilly t rest, move towrds ech other, under mutul force of ttrction At n instnce when the speed of A is v nd speed of B is v, the speed of centre of mss (cm) is (008 E) ) Zero ) v ) 5v 4) 4v Ans : Internl forces do not chnge the CM Velocity or speed of centre of mss is zero Two bodies of 6kg nd 4kg msses hve their velocity 5iˆ ˆ+ 0kˆ nd 0iˆ ˆ+ 5kˆ respectively Then the velocity of their centre of mss is (007 E) ) 5iˆ+ ˆ 8kˆ ) 7iˆ+ ˆ 8kˆ ) 7iˆ ˆ+ 8kˆ 4) 5iˆ ˆ+ 8kˆ Ans : m 6kg, m 4kg V ˆ ˆ ˆ 5i + 0k, V ˆ ˆ ˆ 0i + 5k + mv Velocity of centre of mss VCM m+ m 7iˆ+ ˆ 8kˆ The centre of mss of three prticle s of msses kg, kg, nd kg is t (,, ) The position of the fourth mss of 4kg to be plced in the system so tht the new centre of mss is t (0, 0, 0) is (005 E) (,, ) (,, ) (,, ) 4 (,, ) Ans: As the cm of three prticles is t (,,) The totl mss ++ 6kg Now consider the 4kg mss t the position (x,y,z) Now centre of mss of totl system t (0,0,0) x 0-4x x - 0 Similrly y 0 y z 0 z - From the bove we cn conclude tht x -, y -, z -

2 4 Two prticles of equl mss hve velocities V ccelertion - Centre of mss 4 i nd V 4 First prticle hs n - - (5i + 5 ) ms while the ccelertion of the other prticle is zero The centre of mss of the two prticles moves in pth of [004 E] Stright line Prbol Circle 4 Ellipse Ans : + mv m ˆ ˆ VCM 4i + 4 iˆ+ ˆ m+ m m m + m m ˆ ˆ CM 5i m 0 m+ m m 5 ˆ ˆ i + Both V c nd c re in the sme direction Hence the centre of mss moves in stright line 5 Two obects of msses 00gm nd 500gm hve velocities of 0i m/s nd i + 5 m/s respectively The velocity of their centre of mss is [00 E] ) 5iˆ 5ˆ ) 5 ˆ 5 ˆ 7 i ) 5ˆ 5 ˆ 5 i + 4) 5ˆ i ˆ 7 7 Ans : + mv VCM m+ m 00( 0iˆ) + 500( iˆ+ 5 ˆ) ˆ 5 ˆ 7 i + 6 Prticles of msses m, m, m nm grms re plced on the sme line t distnces, l, l, l, nl cm from fixed point The distnce of centre of mss of the prticles from the fixed point in centimeters in [00 E] (n+ ) l l nn ( + ll ) l ) ) ) 4) n + nn ( + ll ) Ans : Distnce of centre of mss + + n n m+ m + mn ml + ( m)( l) + ( nm)( nl) m+ m+ + nm ml n m[ n] We know tht n Σ n

3 Centre of mss ( + )( n+ ) n n 6 n( n+ ) n( n+ )( n+ ) 6 l n+ n( n+ ) n Σ n x cm ( ) 7 The velocities of three prticles of msses 0g, 0g nd 50g re 0i, 0 nd 0k respectively The velocity of the centre of mss of the three prticles is (00 E) ) i 5k 0 i+ + k ) 0i k 4) i k Ans: + + ) ( ) mv + mv + mv V CM m+ m + m 0 0iˆ+ 0 0 ˆ+ 50 0kˆ i+ + 5k MEDICAL 8 Four prticles, ech of mss kg re plced t the corners of squre OABC of side m O is the origin of the coordinte system OA nd OC re ligned long positive X-xis nd positive Y-xis respectively The position vector of the centre of mss is (in m ) (006 M) ) iˆ+ ˆ ) ( ˆ ˆ ) i ) ( iˆ ˆ) 4) ( ) i Ans : m+ m + m+ m ycm m + m + m + m 4 By substituting the coordintes we get ˆ i, ycm ˆ

4 Position of cm ( ˆ + ˆ ) Centre of mss i 9 Three prticles ech kg mss re plced t the corners of right ngled tringle AOB, O being the origin of the co ordinte system (OA nd OB) long +ve x-direction nd +ve y direction If the positive vector of the centre of OA OB m (in meters) (005 M) i+ i ) ) ) ( i+ ) 4) (i ) Ans : Given OAOBm, m m m kg Given x 0, x, x 0 y 0, y 0, y + + m+ m + m + + ycm m+ m + m Position vector of cm x ˆ ˆ cm i + ycm i+ 0 Four prticles, ech of mss kg, re plced t the corners of squre of side one meter in the X Y plne If the point of intersection of the digonls of the squre is tken s the origin, the coordintes of the centre of mss re (004 M) (, ) (, ) (, ) 4 (0, 0) Ans: 4 For squre centre of mss is t the point of intersection of digonls If this point is tken t the origin then co-ordintes of the centre of mss is (0,0) One end of thin uniform rod of length L nd mss M is rivetted to the centre of uniform circulr disc of rdius r nd mss M so tht both re coplnr The centre of mss of the combintion from the centre of the disc is (ssume tht the point of ttchment is t the origin) (005 M) L(M + M ) LM (M + M ) LM ) ) ) 4) M (M + M ) LM (M + M ) Ans: The length of the rod L 4

5 Centre of mss L x, x 0 (since cm of the disc is t the origin) + m + m L M + M 0 M + M L M M+ M A system consists of two identicl prticles One prticle is t rest nd the other prticle hs n ccelertion The centre of mss of the system hs n ccelertion of (00 M) ) ) ) 4) 4 Ans:4 Accelertion of centre of mss of the system m + m CM m+ m m m A uniform rod of length one meter is bent t its midpoint to mke 90 0 ngle The distnce of the centre of mss from the centre of the rod is (00 M) ) 6 cm ) 5 cm ) 77 cm 4) zero Ans: 4 As the rod is bent midpoint, both the prts hve equl mss The distnce from the point O to the centres of mss of OA nd OB re 5 cm, 5cm respectively ( ) ( ) CC cm Distnce to the effective centre of mss cm 77 (nerly) 5

PhysicsAndMathsTutor.com

PhysicsAndMathsTutor.com 1. A uniform circulr disc hs mss m, centre O nd rdius. It is free to rotte bout fixed smooth horizontl xis L which lies in the sme plne s the disc nd which is tngentil to the disc t the point A. The disc