146235
A smooth is released at rest on a \(45^{\circ}\) incline and then slides a distance ' \(d\) '. The time taken to slide is ' \(n\) ' times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
B When surface is smooth - \(\mathrm{d}=\frac{1}{2}(\mathrm{~g} \sin \theta) \mathrm{t}_{1}^{2}\) When surface is rough - \(\mathrm{d}=\frac{1}{2}(\mathrm{~g} \sin \theta-\mu \mathrm{g} \cos \theta) \mathrm{t}_{2}^{2}\) Time taken to the block slide on incline plane - \(\mathrm{t}_{1}=\sqrt{\frac{2 \mathrm{~d}}{\mathrm{~g} \sin \theta}}, \quad \mathrm{t}_{2}=\sqrt{\frac{2 \mathrm{~d}}{\mathrm{~g} \sin \theta-\mu \mathrm{g} \cos \theta}}\) According to question, \(\mathrm{t}_{2}=\mathrm{nt}_{1}\) \(n \sqrt{\frac{2 d}{g \sin \theta}}=\sqrt{\frac{2 d}{g \sin \theta-\mu g \cos \theta}}\) \(\mu_{\mathrm{k}}\), applicable here, is coefficient of kinetic friction as the block moves over the inclined plane. \(\mathrm{n}=\frac{1}{\sqrt{1-\mu_{\mathrm{k}}}}\) \(\mathrm{n}^{2}=\frac{1}{1-\mu_{\mathrm{k}}} \quad \text { or } \quad 1-\mu_{\mathrm{k}}=\frac{1}{\mathrm{n}^{2}}\) \(\text { or } \mu_{\mathrm{k}}=1-\frac{1}{\mathrm{n}^{2}}\)
SCRA-2014
Laws of Motion
146237
If the coefficient of static friction between the tyres and road is 0.5 , what is the shortest distance in which an automobile can be stopped when travelling at \(72 \mathrm{~km} / \mathrm{h}\) ?
1 \(50 \mathrm{~m}\)
2 \(60 \mathrm{~m}\)
3 \(40.8 \mathrm{~m}\)
4 \(80.16 \mathrm{~m}\)
Explanation:
C Given, \(\mathrm{v} =0\) \(\mathrm{u} =72 \mathrm{~km} / \mathrm{h}=20 \mathrm{~m} / \mathrm{s}\) \(\mathrm{g} =9.8 \mathrm{~m} / \mathrm{s}^{2}\) Here, frictional force working between road and tyres which is retards the motion of automobile. The static friction \(\left(f_{s}\right)\) working between tyres and road, so frictional force cause the retardation in velocity of automobile. Hence, \(\mathrm{F}=\mathrm{f}_{\mathrm{s}} =\mu \mathrm{R}\) \(=\mu . \mathrm{mg}\) Where \(m\) is the mass of automobile We know that, \(\mathrm{F}=\mathrm{ma}\) \(\mu \mathrm{mg}=\mathrm{ma}\) \(\mathrm{a}=\mu \mathrm{g}\) \(\mathrm{a}=0.5 \mathrm{~g}\) Retardation is \(0.5 \mathrm{~g}\) Let automobile stops at a distance \(\mathrm{x}\), then from third equation of motion- \(v^{2} =u^{2}-2 \text { as }\) \(0^{2} =(20)^{2}-2 \times(0.5 \times 9.8) x\) \(x =\frac{20 \times 20}{2 \times 0.5 \times 9.8}=40.8 \mathrm{~m}\) \(\therefore \quad 0^{2}=(20)^{2}-2 \times(0.5 \times 9.8) \mathrm{x}\)
BCECE-2007
Laws of Motion
146232
Assertion: Mountain roads rarely go straight up the slope. Reason: Slope of mountains are large, therefore more chances of vehicle to slip from roads.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
A Therefore, mountain roads rarely go straight up the slope because slope of mountain are large so there are more chances for vehicles to slip from roads.
AIIMS-2016
Laws of Motion
146233
Assertion: Use of ball bearings between two moving parts of a machine is common particle. Reason: Ball bearings reduce vibrations and provide good stability.
1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Explanation:
C Ball bearing are used to reduce friction between moving part of machine. Ball bearing are used to convert sliding friction into rolling friction because rolling friction is much lesser than sliding friction.
146235
A smooth is released at rest on a \(45^{\circ}\) incline and then slides a distance ' \(d\) '. The time taken to slide is ' \(n\) ' times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
B When surface is smooth - \(\mathrm{d}=\frac{1}{2}(\mathrm{~g} \sin \theta) \mathrm{t}_{1}^{2}\) When surface is rough - \(\mathrm{d}=\frac{1}{2}(\mathrm{~g} \sin \theta-\mu \mathrm{g} \cos \theta) \mathrm{t}_{2}^{2}\) Time taken to the block slide on incline plane - \(\mathrm{t}_{1}=\sqrt{\frac{2 \mathrm{~d}}{\mathrm{~g} \sin \theta}}, \quad \mathrm{t}_{2}=\sqrt{\frac{2 \mathrm{~d}}{\mathrm{~g} \sin \theta-\mu \mathrm{g} \cos \theta}}\) According to question, \(\mathrm{t}_{2}=\mathrm{nt}_{1}\) \(n \sqrt{\frac{2 d}{g \sin \theta}}=\sqrt{\frac{2 d}{g \sin \theta-\mu g \cos \theta}}\) \(\mu_{\mathrm{k}}\), applicable here, is coefficient of kinetic friction as the block moves over the inclined plane. \(\mathrm{n}=\frac{1}{\sqrt{1-\mu_{\mathrm{k}}}}\) \(\mathrm{n}^{2}=\frac{1}{1-\mu_{\mathrm{k}}} \quad \text { or } \quad 1-\mu_{\mathrm{k}}=\frac{1}{\mathrm{n}^{2}}\) \(\text { or } \mu_{\mathrm{k}}=1-\frac{1}{\mathrm{n}^{2}}\)
SCRA-2014
Laws of Motion
146237
If the coefficient of static friction between the tyres and road is 0.5 , what is the shortest distance in which an automobile can be stopped when travelling at \(72 \mathrm{~km} / \mathrm{h}\) ?
1 \(50 \mathrm{~m}\)
2 \(60 \mathrm{~m}\)
3 \(40.8 \mathrm{~m}\)
4 \(80.16 \mathrm{~m}\)
Explanation:
C Given, \(\mathrm{v} =0\) \(\mathrm{u} =72 \mathrm{~km} / \mathrm{h}=20 \mathrm{~m} / \mathrm{s}\) \(\mathrm{g} =9.8 \mathrm{~m} / \mathrm{s}^{2}\) Here, frictional force working between road and tyres which is retards the motion of automobile. The static friction \(\left(f_{s}\right)\) working between tyres and road, so frictional force cause the retardation in velocity of automobile. Hence, \(\mathrm{F}=\mathrm{f}_{\mathrm{s}} =\mu \mathrm{R}\) \(=\mu . \mathrm{mg}\) Where \(m\) is the mass of automobile We know that, \(\mathrm{F}=\mathrm{ma}\) \(\mu \mathrm{mg}=\mathrm{ma}\) \(\mathrm{a}=\mu \mathrm{g}\) \(\mathrm{a}=0.5 \mathrm{~g}\) Retardation is \(0.5 \mathrm{~g}\) Let automobile stops at a distance \(\mathrm{x}\), then from third equation of motion- \(v^{2} =u^{2}-2 \text { as }\) \(0^{2} =(20)^{2}-2 \times(0.5 \times 9.8) x\) \(x =\frac{20 \times 20}{2 \times 0.5 \times 9.8}=40.8 \mathrm{~m}\) \(\therefore \quad 0^{2}=(20)^{2}-2 \times(0.5 \times 9.8) \mathrm{x}\)
BCECE-2007
Laws of Motion
146232
Assertion: Mountain roads rarely go straight up the slope. Reason: Slope of mountains are large, therefore more chances of vehicle to slip from roads.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
A Therefore, mountain roads rarely go straight up the slope because slope of mountain are large so there are more chances for vehicles to slip from roads.
AIIMS-2016
Laws of Motion
146233
Assertion: Use of ball bearings between two moving parts of a machine is common particle. Reason: Ball bearings reduce vibrations and provide good stability.
1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Explanation:
C Ball bearing are used to reduce friction between moving part of machine. Ball bearing are used to convert sliding friction into rolling friction because rolling friction is much lesser than sliding friction.
146235
A smooth is released at rest on a \(45^{\circ}\) incline and then slides a distance ' \(d\) '. The time taken to slide is ' \(n\) ' times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
B When surface is smooth - \(\mathrm{d}=\frac{1}{2}(\mathrm{~g} \sin \theta) \mathrm{t}_{1}^{2}\) When surface is rough - \(\mathrm{d}=\frac{1}{2}(\mathrm{~g} \sin \theta-\mu \mathrm{g} \cos \theta) \mathrm{t}_{2}^{2}\) Time taken to the block slide on incline plane - \(\mathrm{t}_{1}=\sqrt{\frac{2 \mathrm{~d}}{\mathrm{~g} \sin \theta}}, \quad \mathrm{t}_{2}=\sqrt{\frac{2 \mathrm{~d}}{\mathrm{~g} \sin \theta-\mu \mathrm{g} \cos \theta}}\) According to question, \(\mathrm{t}_{2}=\mathrm{nt}_{1}\) \(n \sqrt{\frac{2 d}{g \sin \theta}}=\sqrt{\frac{2 d}{g \sin \theta-\mu g \cos \theta}}\) \(\mu_{\mathrm{k}}\), applicable here, is coefficient of kinetic friction as the block moves over the inclined plane. \(\mathrm{n}=\frac{1}{\sqrt{1-\mu_{\mathrm{k}}}}\) \(\mathrm{n}^{2}=\frac{1}{1-\mu_{\mathrm{k}}} \quad \text { or } \quad 1-\mu_{\mathrm{k}}=\frac{1}{\mathrm{n}^{2}}\) \(\text { or } \mu_{\mathrm{k}}=1-\frac{1}{\mathrm{n}^{2}}\)
SCRA-2014
Laws of Motion
146237
If the coefficient of static friction between the tyres and road is 0.5 , what is the shortest distance in which an automobile can be stopped when travelling at \(72 \mathrm{~km} / \mathrm{h}\) ?
1 \(50 \mathrm{~m}\)
2 \(60 \mathrm{~m}\)
3 \(40.8 \mathrm{~m}\)
4 \(80.16 \mathrm{~m}\)
Explanation:
C Given, \(\mathrm{v} =0\) \(\mathrm{u} =72 \mathrm{~km} / \mathrm{h}=20 \mathrm{~m} / \mathrm{s}\) \(\mathrm{g} =9.8 \mathrm{~m} / \mathrm{s}^{2}\) Here, frictional force working between road and tyres which is retards the motion of automobile. The static friction \(\left(f_{s}\right)\) working between tyres and road, so frictional force cause the retardation in velocity of automobile. Hence, \(\mathrm{F}=\mathrm{f}_{\mathrm{s}} =\mu \mathrm{R}\) \(=\mu . \mathrm{mg}\) Where \(m\) is the mass of automobile We know that, \(\mathrm{F}=\mathrm{ma}\) \(\mu \mathrm{mg}=\mathrm{ma}\) \(\mathrm{a}=\mu \mathrm{g}\) \(\mathrm{a}=0.5 \mathrm{~g}\) Retardation is \(0.5 \mathrm{~g}\) Let automobile stops at a distance \(\mathrm{x}\), then from third equation of motion- \(v^{2} =u^{2}-2 \text { as }\) \(0^{2} =(20)^{2}-2 \times(0.5 \times 9.8) x\) \(x =\frac{20 \times 20}{2 \times 0.5 \times 9.8}=40.8 \mathrm{~m}\) \(\therefore \quad 0^{2}=(20)^{2}-2 \times(0.5 \times 9.8) \mathrm{x}\)
BCECE-2007
Laws of Motion
146232
Assertion: Mountain roads rarely go straight up the slope. Reason: Slope of mountains are large, therefore more chances of vehicle to slip from roads.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
A Therefore, mountain roads rarely go straight up the slope because slope of mountain are large so there are more chances for vehicles to slip from roads.
AIIMS-2016
Laws of Motion
146233
Assertion: Use of ball bearings between two moving parts of a machine is common particle. Reason: Ball bearings reduce vibrations and provide good stability.
1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Explanation:
C Ball bearing are used to reduce friction between moving part of machine. Ball bearing are used to convert sliding friction into rolling friction because rolling friction is much lesser than sliding friction.
146235
A smooth is released at rest on a \(45^{\circ}\) incline and then slides a distance ' \(d\) '. The time taken to slide is ' \(n\) ' times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
B When surface is smooth - \(\mathrm{d}=\frac{1}{2}(\mathrm{~g} \sin \theta) \mathrm{t}_{1}^{2}\) When surface is rough - \(\mathrm{d}=\frac{1}{2}(\mathrm{~g} \sin \theta-\mu \mathrm{g} \cos \theta) \mathrm{t}_{2}^{2}\) Time taken to the block slide on incline plane - \(\mathrm{t}_{1}=\sqrt{\frac{2 \mathrm{~d}}{\mathrm{~g} \sin \theta}}, \quad \mathrm{t}_{2}=\sqrt{\frac{2 \mathrm{~d}}{\mathrm{~g} \sin \theta-\mu \mathrm{g} \cos \theta}}\) According to question, \(\mathrm{t}_{2}=\mathrm{nt}_{1}\) \(n \sqrt{\frac{2 d}{g \sin \theta}}=\sqrt{\frac{2 d}{g \sin \theta-\mu g \cos \theta}}\) \(\mu_{\mathrm{k}}\), applicable here, is coefficient of kinetic friction as the block moves over the inclined plane. \(\mathrm{n}=\frac{1}{\sqrt{1-\mu_{\mathrm{k}}}}\) \(\mathrm{n}^{2}=\frac{1}{1-\mu_{\mathrm{k}}} \quad \text { or } \quad 1-\mu_{\mathrm{k}}=\frac{1}{\mathrm{n}^{2}}\) \(\text { or } \mu_{\mathrm{k}}=1-\frac{1}{\mathrm{n}^{2}}\)
SCRA-2014
Laws of Motion
146237
If the coefficient of static friction between the tyres and road is 0.5 , what is the shortest distance in which an automobile can be stopped when travelling at \(72 \mathrm{~km} / \mathrm{h}\) ?
1 \(50 \mathrm{~m}\)
2 \(60 \mathrm{~m}\)
3 \(40.8 \mathrm{~m}\)
4 \(80.16 \mathrm{~m}\)
Explanation:
C Given, \(\mathrm{v} =0\) \(\mathrm{u} =72 \mathrm{~km} / \mathrm{h}=20 \mathrm{~m} / \mathrm{s}\) \(\mathrm{g} =9.8 \mathrm{~m} / \mathrm{s}^{2}\) Here, frictional force working between road and tyres which is retards the motion of automobile. The static friction \(\left(f_{s}\right)\) working between tyres and road, so frictional force cause the retardation in velocity of automobile. Hence, \(\mathrm{F}=\mathrm{f}_{\mathrm{s}} =\mu \mathrm{R}\) \(=\mu . \mathrm{mg}\) Where \(m\) is the mass of automobile We know that, \(\mathrm{F}=\mathrm{ma}\) \(\mu \mathrm{mg}=\mathrm{ma}\) \(\mathrm{a}=\mu \mathrm{g}\) \(\mathrm{a}=0.5 \mathrm{~g}\) Retardation is \(0.5 \mathrm{~g}\) Let automobile stops at a distance \(\mathrm{x}\), then from third equation of motion- \(v^{2} =u^{2}-2 \text { as }\) \(0^{2} =(20)^{2}-2 \times(0.5 \times 9.8) x\) \(x =\frac{20 \times 20}{2 \times 0.5 \times 9.8}=40.8 \mathrm{~m}\) \(\therefore \quad 0^{2}=(20)^{2}-2 \times(0.5 \times 9.8) \mathrm{x}\)
BCECE-2007
Laws of Motion
146232
Assertion: Mountain roads rarely go straight up the slope. Reason: Slope of mountains are large, therefore more chances of vehicle to slip from roads.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
A Therefore, mountain roads rarely go straight up the slope because slope of mountain are large so there are more chances for vehicles to slip from roads.
AIIMS-2016
Laws of Motion
146233
Assertion: Use of ball bearings between two moving parts of a machine is common particle. Reason: Ball bearings reduce vibrations and provide good stability.
1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Explanation:
C Ball bearing are used to reduce friction between moving part of machine. Ball bearing are used to convert sliding friction into rolling friction because rolling friction is much lesser than sliding friction.
