Rigid Body Constraints
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366063 A rigid body is rolling without sliping on the horizontal surface, then match the Column I with Column II and select the correct answer from the codes given below.
Column I
Column II
A
Velocity at point A
P
\(\sqrt 2 v\)
B
Velocity at point B
Q
\(0\)
C
Velocity at point C
R
\(v\sqrt {2 - \sqrt 2 } \)
D
Velocity at point D
S
\(2v\)
supporting img

1 \({\rm{A}}\, - {\rm{Q,}}\,\,{\rm{B}}\,\, - \,{\rm{P,}}\,\,{\rm{C}} - \,\,{\rm{S,}}\,\,\,{\rm{D}} - {\rm{R}}\)
2 \({\rm{A}} - {\rm{P}},\,\,{\rm{B}} - {\rm{R}},\,\,{\rm{C}} - {\rm{S}},\,\,\,D - Q\)
3 \({\rm{A}} - {\rm{S}},\,\,{\rm{B}} - {\rm{R}},\,\,{\rm{C}} - {\rm{Q}},\,\,D - P\)
4 \({\rm{A}} - {\rm{Q}},\,{\rm{B}} - {\rm{R}},\,\,{\rm{C}} - {\rm{S}},\,\,D - P\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366064 A pulley of radius \(R\) is unwinding with the downward linear acceleration \(a\) and angular acceleration \(\alpha\). If the string is unstretchable and there is no slipping between the string and the pulley, then the relation between \(a\) and \(\alpha\) is
supporting img

1 \(a=\dfrac{R \alpha}{2}\)
2 \(a < R \alpha\)
3 \(a=R \alpha\)
4 \(a>R \alpha\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366065 A bobbin is pushed along on a rough stationary horizontal surface as shown in the figure. The board is kept horizontal and there is no slipping at any contact points. The distance moved by the axis of the bobbin is \(l\). The distance travelled by the board \((\mathrm{B})\) is
supporting img

1 \(l\left(1+\dfrac{r}{R}\right)\)
2 \(l\left(1+\dfrac{2 r}{R}\right)\)
3 \(l\left(2+\dfrac{r}{R}\right)\)
4 \(l\left(1+\dfrac{r}{2 R}\right)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366066 Velocity of the centre of a small cylinder is \(v\). There is no slipping anywhere. The velocity of the centre of the larger cylinder is
supporting img

1 \(v\)
2 \(\dfrac{3 v}{2}\)
3 \(2 v\)
4 None of these
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366063 A rigid body is rolling without sliping on the horizontal surface, then match the Column I with Column II and select the correct answer from the codes given below.
Column I
Column II
A
Velocity at point A
P
\(\sqrt 2 v\)
B
Velocity at point B
Q
\(0\)
C
Velocity at point C
R
\(v\sqrt {2 - \sqrt 2 } \)
D
Velocity at point D
S
\(2v\)
supporting img

1 \({\rm{A}}\, - {\rm{Q,}}\,\,{\rm{B}}\,\, - \,{\rm{P,}}\,\,{\rm{C}} - \,\,{\rm{S,}}\,\,\,{\rm{D}} - {\rm{R}}\)
2 \({\rm{A}} - {\rm{P}},\,\,{\rm{B}} - {\rm{R}},\,\,{\rm{C}} - {\rm{S}},\,\,\,D - Q\)
3 \({\rm{A}} - {\rm{S}},\,\,{\rm{B}} - {\rm{R}},\,\,{\rm{C}} - {\rm{Q}},\,\,D - P\)
4 \({\rm{A}} - {\rm{Q}},\,{\rm{B}} - {\rm{R}},\,\,{\rm{C}} - {\rm{S}},\,\,D - P\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366064 A pulley of radius \(R\) is unwinding with the downward linear acceleration \(a\) and angular acceleration \(\alpha\). If the string is unstretchable and there is no slipping between the string and the pulley, then the relation between \(a\) and \(\alpha\) is
supporting img

1 \(a=\dfrac{R \alpha}{2}\)
2 \(a < R \alpha\)
3 \(a=R \alpha\)
4 \(a>R \alpha\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366065 A bobbin is pushed along on a rough stationary horizontal surface as shown in the figure. The board is kept horizontal and there is no slipping at any contact points. The distance moved by the axis of the bobbin is \(l\). The distance travelled by the board \((\mathrm{B})\) is
supporting img

1 \(l\left(1+\dfrac{r}{R}\right)\)
2 \(l\left(1+\dfrac{2 r}{R}\right)\)
3 \(l\left(2+\dfrac{r}{R}\right)\)
4 \(l\left(1+\dfrac{r}{2 R}\right)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366066 Velocity of the centre of a small cylinder is \(v\). There is no slipping anywhere. The velocity of the centre of the larger cylinder is
supporting img

1 \(v\)
2 \(\dfrac{3 v}{2}\)
3 \(2 v\)
4 None of these
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366063 A rigid body is rolling without sliping on the horizontal surface, then match the Column I with Column II and select the correct answer from the codes given below.
Column I
Column II
A
Velocity at point A
P
\(\sqrt 2 v\)
B
Velocity at point B
Q
\(0\)
C
Velocity at point C
R
\(v\sqrt {2 - \sqrt 2 } \)
D
Velocity at point D
S
\(2v\)
supporting img

1 \({\rm{A}}\, - {\rm{Q,}}\,\,{\rm{B}}\,\, - \,{\rm{P,}}\,\,{\rm{C}} - \,\,{\rm{S,}}\,\,\,{\rm{D}} - {\rm{R}}\)
2 \({\rm{A}} - {\rm{P}},\,\,{\rm{B}} - {\rm{R}},\,\,{\rm{C}} - {\rm{S}},\,\,\,D - Q\)
3 \({\rm{A}} - {\rm{S}},\,\,{\rm{B}} - {\rm{R}},\,\,{\rm{C}} - {\rm{Q}},\,\,D - P\)
4 \({\rm{A}} - {\rm{Q}},\,{\rm{B}} - {\rm{R}},\,\,{\rm{C}} - {\rm{S}},\,\,D - P\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366064 A pulley of radius \(R\) is unwinding with the downward linear acceleration \(a\) and angular acceleration \(\alpha\). If the string is unstretchable and there is no slipping between the string and the pulley, then the relation between \(a\) and \(\alpha\) is
supporting img

1 \(a=\dfrac{R \alpha}{2}\)
2 \(a < R \alpha\)
3 \(a=R \alpha\)
4 \(a>R \alpha\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366065 A bobbin is pushed along on a rough stationary horizontal surface as shown in the figure. The board is kept horizontal and there is no slipping at any contact points. The distance moved by the axis of the bobbin is \(l\). The distance travelled by the board \((\mathrm{B})\) is
supporting img

1 \(l\left(1+\dfrac{r}{R}\right)\)
2 \(l\left(1+\dfrac{2 r}{R}\right)\)
3 \(l\left(2+\dfrac{r}{R}\right)\)
4 \(l\left(1+\dfrac{r}{2 R}\right)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366066 Velocity of the centre of a small cylinder is \(v\). There is no slipping anywhere. The velocity of the centre of the larger cylinder is
supporting img

1 \(v\)
2 \(\dfrac{3 v}{2}\)
3 \(2 v\)
4 None of these
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366063 A rigid body is rolling without sliping on the horizontal surface, then match the Column I with Column II and select the correct answer from the codes given below.
Column I
Column II
A
Velocity at point A
P
\(\sqrt 2 v\)
B
Velocity at point B
Q
\(0\)
C
Velocity at point C
R
\(v\sqrt {2 - \sqrt 2 } \)
D
Velocity at point D
S
\(2v\)
supporting img

1 \({\rm{A}}\, - {\rm{Q,}}\,\,{\rm{B}}\,\, - \,{\rm{P,}}\,\,{\rm{C}} - \,\,{\rm{S,}}\,\,\,{\rm{D}} - {\rm{R}}\)
2 \({\rm{A}} - {\rm{P}},\,\,{\rm{B}} - {\rm{R}},\,\,{\rm{C}} - {\rm{S}},\,\,\,D - Q\)
3 \({\rm{A}} - {\rm{S}},\,\,{\rm{B}} - {\rm{R}},\,\,{\rm{C}} - {\rm{Q}},\,\,D - P\)
4 \({\rm{A}} - {\rm{Q}},\,{\rm{B}} - {\rm{R}},\,\,{\rm{C}} - {\rm{S}},\,\,D - P\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366064 A pulley of radius \(R\) is unwinding with the downward linear acceleration \(a\) and angular acceleration \(\alpha\). If the string is unstretchable and there is no slipping between the string and the pulley, then the relation between \(a\) and \(\alpha\) is
supporting img

1 \(a=\dfrac{R \alpha}{2}\)
2 \(a < R \alpha\)
3 \(a=R \alpha\)
4 \(a>R \alpha\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366065 A bobbin is pushed along on a rough stationary horizontal surface as shown in the figure. The board is kept horizontal and there is no slipping at any contact points. The distance moved by the axis of the bobbin is \(l\). The distance travelled by the board \((\mathrm{B})\) is
supporting img

1 \(l\left(1+\dfrac{r}{R}\right)\)
2 \(l\left(1+\dfrac{2 r}{R}\right)\)
3 \(l\left(2+\dfrac{r}{R}\right)\)
4 \(l\left(1+\dfrac{r}{2 R}\right)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366066 Velocity of the centre of a small cylinder is \(v\). There is no slipping anywhere. The velocity of the centre of the larger cylinder is
supporting img

1 \(v\)
2 \(\dfrac{3 v}{2}\)
3 \(2 v\)
4 None of these