Q: There are two inclined surface of equal length (L) and same angle of inclination 45^ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much tim

aligned & L= 1 2 a_S t_S^2= 1 2 a_R t_R^2 \\ & ( t_ s t_R )^2= a_R a_ S \\ & ( 1 2 )^2= g - _k g g \\ & 1 4 = 45^ - _k 45^ 45^ \\ & 1 4 = ( 1 2 ) ( 1 2 ) ( 1- _k 1 ) \\ & 1 4 =1- _k _k=1- 1 4 = 3 4 =0.75 aligned

Q: A horizontal force 10 N is applied to a block A as shown in figure. The mass of blocks A and B are 2 kg and 3 kg respectively. The blocks slide over a frictionless surface. The force exerted by block

aligned & F= (M_1+M_2 ) a \\ & a= 10 2+3 =2 ~ms ^ -2 \\ & F^ =M_2(2)=3 2 ~N =6 ~N aligned

Question 1

The magnitude and direction of the acceleration produced in a body of mass 5 kg when two mutually perpendicular forces 8 N and 6 N act on it, are respectively :

Accepted Answer

Given forces are F_1 = 8 N and F_2 = 6 N acting perpendicular to each other. The magnitude of the net force is F = F_1^2 + F_2^2 = 8^2 + 6^2 = 10 N. The magnitude of acceleration is a = F m = 10 5 = 2 m s^ -2 . Let be the angle made by the net force with the 8 N force. = F_2 F_1 = 6 8 = 3 4 = ^ -1 ( 3 4 ) with the 8 N force. Answer: 2 m s^ -2 ; ^ -1 (3/4) with 8 N force

Question 2

A box of mass 15 kg is kept on the floor of a stationary trolley. The coefficient of static friction between the box and the trolley is 0.12. Keeping the box in stationary state over the trolley, the

Accepted Answer

Let the acceleration of the trolley be a. In the frame of the trolley, a pseudo force ma acts on the box in the direction opposite to the motion. For the box to remain stationary relative to the trolley, the static friction force must balance this pseudo force. The maximum static friction force available is given by f_ s, max = _s N = _s mg. Equating the pseudo force to the maximum static friction force gives the maximum acceleration: ma_ max = _s mg a_ max = _s g Substituting the given values _

Question 3

A car travels on a circular racetrack of radius 50 m, which is banked at an angle . If the car travels at a speed 10 ms^ -1 , then the wear and tear on its tyres is minimum. Taking the acceleration du

Accepted Answer

For minimum wear and tear on the tyres, the frictional force should be zero. The required centripetal force is provided entirely by the horizontal component of the normal reaction. The optimum speed v on a banked road is given by: v = R g Squaring both sides: v^2 = R g Substituting the given values v = 10 ms^ -1 , R = 50 m, and g = 10 ms^ -2 : (10)^2 = 50 10 100 = 500 = 100 500 = 1 5 = ^ -1 ( 1 5 ) Answer: ^ -1 ( 1 5 )

Question 4

There are two inclined surface of equal length (L) and same angle of inclination 45^ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much tim

Accepted Answer

aligned & L= 1 2 a_S t_S^2= 1 2 a_R t_R^2 \ & ( t_ s t_R )^2= a_R a_ S \ & ( 1 2 )^2= g - _k g g \ & 1 4 = 45^ - _k 45^ 45^ \ & 1 4 = ( 1 2 ) ( 1 2 ) ( 1- _k 1 ) \ & 1 4 =1- _k _k=1- 1 4 = 3 4 =0.75 aligned

Question 5

A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an angle of 60^ with it. The other end rests on a rough horizontal floor. The friction force that the floor exert

Accepted Answer

N _2= mg =200 ~N Taking torque about A : aligned & f _ s ~L 60^ + mg ~L 2 60^ = N _2 ~L 60^ \ & f _ s ( 1 2 )+200 ( 1 2 ) 3 2 =200 3 2 \ & f _ s =100 3 ~N aligned

Question 6

A box of mass 5 kg is pulled by a cord, up along a frictionless plane inclined at 30^ with the horizontal. The tension in the cord is 30 N . The acceleration of the box is (Take g=10 ~m ~s ^ -2 )

Accepted Answer

T-M g 30=M a 30-5 10 1 2 =5 a a=1 ~m / s ^2

Question 7

A bob is whirled in a horizontal circle by means of a string at an initial speed of 10 rpm. If the tension in the string is quadrupled while keeping the radius constant, the new speed is:

Accepted Answer

In horizontal circular motion, T=m ^2 r For constant m and r, T ^2 T=4 T (Given) ^ =2 =20 rpm

Question 8

A horizontal force 10 N is applied to a block A as shown in figure. The mass of blocks A and B are 2 kg and 3 kg respectively. The blocks slide over a frictionless surface. The force exerted by block

Accepted Answer

aligned & F= (M_1+M_2 ) a \ & a= 10 2+3 =2 ~ms ^ -2 \ & F^ =M_2(2)=3 2 ~N =6 ~N aligned

Laws of Motion — Previous Year Questions & Solutions