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Hubert Francis
5 years ago
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1 Iclied Plae. A give object takes times as much time to slide dow a 45 0 rough iclied plae as it takes to slide dow a perfectly smooth 45 0 iclie. The coefficiet of kietic frictio betwee the object ad the iclie is () () () (4). A block of mass M is restig o a iclied plae. Whe the agle of icliatio is gradually icreased toθ, the block just begis to slide dow the plae. What miimum force applied parallel to the plae o the block would just make the block move up the plae? () Mg siθ () Mg cosθ () Mg cosθ (4) Mg siθ. A cylider rolls up a iclied plae, reaches some height ad the rolls dow (without slippig through out these motios). The directios of frictioal force actig o the cylider are ) Up the iclie while ascedig ad dow the iclie while descedig ) Up the iclie while ascedig as well as descedig ) Dow the iclie while ascedig ad up the iclie while descedig 4) Dow the iclie while ascedig as well as descedig 4. Cosider the followig A ad B, ad idetify the correct choice i the give aswers. A) For a body restig o a rough horizotal table, it is easier to pull at agle that pushes at the same agle to cause motio. B) A body slidig dow a rough iclied plae of icliatio equal to agle of frictio has o-zero acceleratio. ) Both A ad B are true.

2 ) A is true but B is false. ) A is false but B is true. 4) Both A ad B are false. 5. (A): The time of ascet for a body projected to move up a rough iclied plae is less tha the time of descet. (R): The retardatio for upward motio is more tha the acceleratio for dowward motio. () Both (A) ad (R) are true ad (R) is the correct explaatio of (A). () Both (A) ad (R) are true ad (R) is ot the correct explaatio of (A). () (A) is true but (R) is false. (4) (A) is false but (R) is true. 6. A block is pushed up a rough iclied plae of 45. If the time of descet is twice the time of ascet, the coefficiet of frictio is ) 0.6 ) 0.4 ) 0.5 4) The miimum force required to move a body up a iclied plae is three times the miimum force required to prevet it from slidig dow the plae. If coefficiet of frictio betwee the body ad iclied plae is, the agle of iclied plae is ) 60º ) 45º ) 0º 4) 5º 8. A block slides dow a rough iclied plae of slope agle with costat velocity. It is the projected up the same plae with a iitial velocity v. The distace travelled by the block up the plae before comig to rest is, v v v 4gv gsiθ gsiθ gsiθ siθ

3 9. Sad is piled up o a horizotal groud i the form of a regular coe of a fixed base radius R. The coefficiet of static frictio betwee sad layers isμ. The maximum volume of sad that ca be piled up, without the sad slippig o the surface is ) μr π ) μr π R ) μ 4) μ π R 0. A body is movig up a iclied plae of agle θ with a iitial kietic eergy E. The coefficiet of frictio betwee the plae ad body is m. The work doe agaist frictio before the body comes to rest is (00 E) ) μ cosθ E cosθ + siθ ) μe cosθ ) μe cosθ μ cosθ siθ 4) μe cosθ μ cosθ + siθ. A block of mass kg is lyig o a iclied plae at a agle of 0 o with the horizotal the coefficiet of frictio betwee the block ad the plae is 0.7 the frictioal force actig o the iclied plae will be () Zero () 9.8N () 9.8 x N (4) 9.8 x 0.7x N. A object of mass kg slides dow a iclied plae which makes a agle of 0 o with the horizotal. The coefficiet of frictio betwee the object ad the surface is the force applied to the object so that the object moves dow o the surface with a uiform speed is ().N () 5N () 5N (4) Noe. A particle is projected up a 45 o rough iclie with a velocity v. The coefficiet of frictio is 0.5 the speed with which it returs back to the straight poit is v v the v is () () () (4)

4 4. A body slides dow a rough iclied plae of agle of icliatio 0 o ad takes times twice as great as the time take i slippig dow a similar frictioless plae. The coefficiet of frictio betwee the body ad the plae is () 4 () () 4 (4) 4 5. A body slides dow a rough iclied plae of agle of icliatio 0º ad takes time twice as great as the time take i slippig dow a idetical frictioless plae. The coefficiet of frictio betwee the body ad the plae is. /4.. 4/ 4. ¾ 6. A body slides dow a smooth iclied plae of height h ad agle of icliatio 0º reactig the bottom with a velocity v. Without chagig the height, if the agle of icliatio is doubled, the velocity with which it reaches the bottom of the plae is. Vv. v/. v 4. v 7. A particle is projected up alog a rough plae of icliatio 45º with the horizotal. If the coefficiet of frictio is 0.5, the retardatio is (g = acceleratio due to gravity). g g.. g 8. The miimum force required to move a body up a iclied plae of icliatio 0º is foud to be thrice the miimum force required to prevet it from slidig dow the plae. The coefficiet of frictio betwee the body ad the plae is. /. /. / 4. /4 9. A block takes twice as much time to slide dow a rough takes to slide dow a idetical smooth 4. g 0 45 iclied plae as it 0 45 iclied plae. The coefficiet of kietic frictio betwee the block ad the rough iclied plae is ) 0.5 ) 0.5 ) ).0

5 0. A body of mass m projected vertically upwards with a iitial velocity u reaches a maximum height h. Aother body of mass m is projected alog a iclied plae makig a agle 0º with the horizotal ad with speed u. The maximum distace travelled alog the iclie is h. h. h.. A body is slidig dow a iclied plae havig coefficiet of frictio 0.5. If the ormal reactio is twice that of the resultat dowward force alog the iclie, the agle betwee the iclied plae ad horizotal is. 5º. 0º. 45º 4. 60º. A body takes four third times as much time to slide dow rough iclied plae as it takes to side dow a idetical but smooth iclied plae if the agle of iclied plae is 45º. The coefficiet of frictio is. 7/6. 9/6. 7/9 4. ¾. A 0kg box has to move up a iclied slope of 0º to horizotal at a uiform velocity of 5 m/sec. If the frictioal force retardig the motio is 50N the horizotal force to move up is (g=0 m/sec ). 00 N. 00N. 00 N/ x / N 4. A body is released from the top of a smooth iclied plae at height h above the groud. Simultaeously aother body is pushed up with a velocity V from the bottom. If they meet after time t, icliatio of that iclied plae to the horizotal is. si hu t. cos hu t. si ut h 4. 4 h hu 4. cos t

6 5. A isect crawls up a hemispherical surface. The coefficiet of frictio betwee the isect ad the surface is /. If the lie joiig the cetre of the hemispherical surface to the isect makes a agle with the vertical, the maximum possible value of α is give by. Cot α =. Ta α =. Sec α = 4. Cosec α = KEY ) ) 4 ) 4) 5) 6) 7) 8) 9) 4 0) 4 )4 ) ) 4) 5) 6) 7) 8) 9) 0) ) ) ) 4 4) 5) 6. t t a 7. α = μ Taθ = + Ta 45 μ = + μ = 0.6 μ Taθ = = + Taθ + = Taθ + 4 Taθ = θ = 0 8. μ = Taθ V s = g (siθ + μcos θ) HINTS

7 V s = g (siθ + taθcosθ V s = 4g siθ 9. μ = Taθ h μ = h= μr R Volume of the cube v= πr h= πr. μr= μπ R 0. Work = f x s u W = μmgcosθ a u W = μmgcosθ g (siθ + μcos θ) μ E cosθ W = (siθ + μcos θ). Frictioal force = µmg cosθ F = 0.7 x x 9.8 x. F r = mg siθ + F R = mg cos θ F = µmg cos θ mg si θ = 0 x0x = 0.7 x 9.8 x N = 0 0 =. N

8 5. μ = ta θ 6. V = gh Ad V does ot depeds o whe h=costat 7. a = g (siθ + μ k cosθ ) 8. mg ( siθ + μcosθ) = mg ( siθ μcosθ) 9. a = gsi 45 = g 0 g a = g(si 45 μk cos 45 ) = μk t α a t t a = ; t = t a Substitutig μ = u = gh u = g l siθ. mg cosθ x = mg si θ. t s k ( ) l l = ; tr = gsiθ g siθ μcosθ ( ). F = mg si θ + mg cos θ Horizotal compoet of force = F cosθ 4. S = g si θt S = ut g si θt S = S+ S=ut

9 θ h si ut = 5. taα = cotα =

04 - LAWS OF MOTION Page 1 ( Answers at the end of all questions )

04 - LAWS OF MOTION Page 1 ( Answers at the end of all questions ) 04 - LAWS OF MOTION Page ) A smooth block is released at rest o a 45 iclie ad the slides a distace d. The time take to slide is times as much to slide o rough iclie tha o a smooth iclie. The coefficiet