1
Question
A cylinder of radius 1 m rolls on the planks A and B without relative sliding. If the planks move with velocities −4^im/s and 2^im/s respectively and the plank A has acceleration →a(=2^im/s2). Match the entries in column 1 to entries of column 2
Column-I Column-II
i vC( in m/s) p −^i−3^j ii vQ( in m/s) q −^i iii aC( in m/s2) r ^i iv aQ( in m/s2) s −8^i+2^j
A cylinder of radius 1 m rolls on the planks A and B without relative sliding. If the planks move with velocities −4^im/s and 2^im/s respectively and the plank A has acceleration →a(=2^im/s2). Match the entries in column 1 to entries of column 2
Column-I Column-II
| i | vC( in m/s) | p | −^i−3^j |
| ii | vQ( in m/s) | q | −^i |
| iii | aC( in m/s2) | r | ^i |
| iv | aQ( in m/s2) | s | −8^i+2^j |
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Solution
The correct option is B i-q ; ii-p ; iii-r ; iv-s
→vC=→vCB+→vB=−Rω^i+v^i=[−R(3v2R)+v]^i=−v2^i=−^im/s→vQ=→vQC+→vVC=−Rω^j−v2^i=−R(3v2R)^j−v2^i=−32v^j−v2^i=−^i−3^jm/s
aC=a2^i=^im/s2¯¯¯aQ=¯¯¯aQC+¯¯¯aCB+¯¯¯aB=−Rω2^i+Rα^j+a2^i where α=a2R and ω=3v2R→aQ=(a2−9v24R)^i+a2^j=−8^i+2^jm/s2
→vC=→vCB+→vB=−Rω^i+v^i=[−R(3v2R)+v]^i=−v2^i=−^im/s→vQ=→vQC+→vVC=−Rω^j−v2^i=−R(3v2R)^j−v2^i=−32v^j−v2^i=−^i−3^jm/s
aC=a2^i=^im/s2¯¯¯aQ=¯¯¯aQC+¯¯¯aCB+¯¯¯aB=−Rω2^i+Rα^j+a2^i where α=a2R and ω=3v2R→aQ=(a2−9v24R)^i+a2^j=−8^i+2^jm/s2