Friction, and Inclined Plane Friction Motion
LAWS OF MOTION (ADDITIONAL)

372154 A bullet of mass of \(0.02 \quad \mathrm{~kg}\) travelling horizontally with velocity \(250 \mathrm{~ms}^{-1}\) strikes a block of wood of mass \(0.23 \mathrm{~kg}\) which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after travelling a distance of \(40 \mathrm{~m}\). The coefficient of sliding friction of the rough surface is \(\left(g=9.8 \mathrm{~ms}^{-2}\right)\)

1 0.75
2 0.61
3 0.51
4 0.30
LAWS OF MOTION (ADDITIONAL)

372155 When the engine is switched off a vehicle of mass \(M\) is moving on a rough horizontal road with momentum \(p\). If the coefficient of friction between the road and tyres of the vehicle is \(\mu_{\mathrm{k}}\), the distance travelled by the vehicle before it comes to rest is

1 \(\frac{p^{2}}{2 \mu_{k} M^{2} g}\)
2 \(\frac{2 \mu_{\mathrm{k}} \mathrm{M}^{2} \mathrm{~g}}{\mathrm{p}^{2}}\)
3 \(\frac{\mathrm{p}^{2}}{2 \mu_{\mathrm{k}} \mathrm{g}}\)
4 \(\frac{p^{2} M^{2}}{2 \mu_{k} g}\)
LAWS OF MOTION (ADDITIONAL)

372156 A uniform circular disc of radius \(R\), lying on a frictionless horizontal plane is rotating with an angular velocity ' \(\omega\) ' about is its own axis. Another identical circular disc is gently placed on the top of the first disc coaxially. The loss in rotational kinetic energy due to friction between the two discs, as they acquire common angular velocity is ( \(I\) is moment of inertia of the disc)

1 \(\frac{1}{8} \mathrm{I} \omega^{2}\)
2 \(\frac{1}{4} \mathrm{I} \omega^{2}\)
3 \(\frac{1}{2} \mathrm{I} \omega^{2}\)
4 \(I \omega^{2}\)
LAWS OF MOTION (ADDITIONAL)

372157 The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction, when the angle of inclination of the plane is \(60^{\circ}\) is

1 \(\frac{1}{3}\)
2 \(\frac{1}{\sqrt{2}}\)
3 \(\frac{1}{\sqrt{3}}\)
4 \(\frac{1}{2}\)
LAWS OF MOTION (ADDITIONAL)

372154 A bullet of mass of \(0.02 \quad \mathrm{~kg}\) travelling horizontally with velocity \(250 \mathrm{~ms}^{-1}\) strikes a block of wood of mass \(0.23 \mathrm{~kg}\) which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after travelling a distance of \(40 \mathrm{~m}\). The coefficient of sliding friction of the rough surface is \(\left(g=9.8 \mathrm{~ms}^{-2}\right)\)

1 0.75
2 0.61
3 0.51
4 0.30
LAWS OF MOTION (ADDITIONAL)

372155 When the engine is switched off a vehicle of mass \(M\) is moving on a rough horizontal road with momentum \(p\). If the coefficient of friction between the road and tyres of the vehicle is \(\mu_{\mathrm{k}}\), the distance travelled by the vehicle before it comes to rest is

1 \(\frac{p^{2}}{2 \mu_{k} M^{2} g}\)
2 \(\frac{2 \mu_{\mathrm{k}} \mathrm{M}^{2} \mathrm{~g}}{\mathrm{p}^{2}}\)
3 \(\frac{\mathrm{p}^{2}}{2 \mu_{\mathrm{k}} \mathrm{g}}\)
4 \(\frac{p^{2} M^{2}}{2 \mu_{k} g}\)
LAWS OF MOTION (ADDITIONAL)

372156 A uniform circular disc of radius \(R\), lying on a frictionless horizontal plane is rotating with an angular velocity ' \(\omega\) ' about is its own axis. Another identical circular disc is gently placed on the top of the first disc coaxially. The loss in rotational kinetic energy due to friction between the two discs, as they acquire common angular velocity is ( \(I\) is moment of inertia of the disc)

1 \(\frac{1}{8} \mathrm{I} \omega^{2}\)
2 \(\frac{1}{4} \mathrm{I} \omega^{2}\)
3 \(\frac{1}{2} \mathrm{I} \omega^{2}\)
4 \(I \omega^{2}\)
LAWS OF MOTION (ADDITIONAL)

372157 The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction, when the angle of inclination of the plane is \(60^{\circ}\) is

1 \(\frac{1}{3}\)
2 \(\frac{1}{\sqrt{2}}\)
3 \(\frac{1}{\sqrt{3}}\)
4 \(\frac{1}{2}\)
LAWS OF MOTION (ADDITIONAL)

372154 A bullet of mass of \(0.02 \quad \mathrm{~kg}\) travelling horizontally with velocity \(250 \mathrm{~ms}^{-1}\) strikes a block of wood of mass \(0.23 \mathrm{~kg}\) which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after travelling a distance of \(40 \mathrm{~m}\). The coefficient of sliding friction of the rough surface is \(\left(g=9.8 \mathrm{~ms}^{-2}\right)\)

1 0.75
2 0.61
3 0.51
4 0.30
LAWS OF MOTION (ADDITIONAL)

372155 When the engine is switched off a vehicle of mass \(M\) is moving on a rough horizontal road with momentum \(p\). If the coefficient of friction between the road and tyres of the vehicle is \(\mu_{\mathrm{k}}\), the distance travelled by the vehicle before it comes to rest is

1 \(\frac{p^{2}}{2 \mu_{k} M^{2} g}\)
2 \(\frac{2 \mu_{\mathrm{k}} \mathrm{M}^{2} \mathrm{~g}}{\mathrm{p}^{2}}\)
3 \(\frac{\mathrm{p}^{2}}{2 \mu_{\mathrm{k}} \mathrm{g}}\)
4 \(\frac{p^{2} M^{2}}{2 \mu_{k} g}\)
LAWS OF MOTION (ADDITIONAL)

372156 A uniform circular disc of radius \(R\), lying on a frictionless horizontal plane is rotating with an angular velocity ' \(\omega\) ' about is its own axis. Another identical circular disc is gently placed on the top of the first disc coaxially. The loss in rotational kinetic energy due to friction between the two discs, as they acquire common angular velocity is ( \(I\) is moment of inertia of the disc)

1 \(\frac{1}{8} \mathrm{I} \omega^{2}\)
2 \(\frac{1}{4} \mathrm{I} \omega^{2}\)
3 \(\frac{1}{2} \mathrm{I} \omega^{2}\)
4 \(I \omega^{2}\)
LAWS OF MOTION (ADDITIONAL)

372157 The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction, when the angle of inclination of the plane is \(60^{\circ}\) is

1 \(\frac{1}{3}\)
2 \(\frac{1}{\sqrt{2}}\)
3 \(\frac{1}{\sqrt{3}}\)
4 \(\frac{1}{2}\)
LAWS OF MOTION (ADDITIONAL)

372154 A bullet of mass of \(0.02 \quad \mathrm{~kg}\) travelling horizontally with velocity \(250 \mathrm{~ms}^{-1}\) strikes a block of wood of mass \(0.23 \mathrm{~kg}\) which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after travelling a distance of \(40 \mathrm{~m}\). The coefficient of sliding friction of the rough surface is \(\left(g=9.8 \mathrm{~ms}^{-2}\right)\)

1 0.75
2 0.61
3 0.51
4 0.30
LAWS OF MOTION (ADDITIONAL)

372155 When the engine is switched off a vehicle of mass \(M\) is moving on a rough horizontal road with momentum \(p\). If the coefficient of friction between the road and tyres of the vehicle is \(\mu_{\mathrm{k}}\), the distance travelled by the vehicle before it comes to rest is

1 \(\frac{p^{2}}{2 \mu_{k} M^{2} g}\)
2 \(\frac{2 \mu_{\mathrm{k}} \mathrm{M}^{2} \mathrm{~g}}{\mathrm{p}^{2}}\)
3 \(\frac{\mathrm{p}^{2}}{2 \mu_{\mathrm{k}} \mathrm{g}}\)
4 \(\frac{p^{2} M^{2}}{2 \mu_{k} g}\)
LAWS OF MOTION (ADDITIONAL)

372156 A uniform circular disc of radius \(R\), lying on a frictionless horizontal plane is rotating with an angular velocity ' \(\omega\) ' about is its own axis. Another identical circular disc is gently placed on the top of the first disc coaxially. The loss in rotational kinetic energy due to friction between the two discs, as they acquire common angular velocity is ( \(I\) is moment of inertia of the disc)

1 \(\frac{1}{8} \mathrm{I} \omega^{2}\)
2 \(\frac{1}{4} \mathrm{I} \omega^{2}\)
3 \(\frac{1}{2} \mathrm{I} \omega^{2}\)
4 \(I \omega^{2}\)
LAWS OF MOTION (ADDITIONAL)

372157 The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction, when the angle of inclination of the plane is \(60^{\circ}\) is

1 \(\frac{1}{3}\)
2 \(\frac{1}{\sqrt{2}}\)
3 \(\frac{1}{\sqrt{3}}\)
4 \(\frac{1}{2}\)
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