Practice Questions

Q1. If two vectors →𝐴 and →𝐵 having equal magnitude 𝑅 are inclined at an angle 𝜃, then 𝜃 2𝑅sin (1) →𝐴− →𝐵= √2𝑅sin 𝜃2 (2) →𝐴+ →𝐵= 2 → → 𝜃 → → 𝜃 (3) 𝐴+ 𝐵= 2𝑅cos (4) 𝐴− 𝐵= 2𝑅cos 2 2

Q2. The dimensional formula of angular impulse is : (1) [M L – 2T – 1] (2) [M L2 T – 2 ] (3) [M L T – 1 ] (4) [M L2 T – 1 ]

Q2. The angle of projection for a projectile to have same horizontal range and maximum height is : (1) tan−1(4) (2) tan−1 ( 14 ) (3) tan−1 ( 21 ) (4) tan−1(2)

Q2. A particle is moving in a straight line. The variation of position x as a function of time t is given as x = (t3 −6t2 + 20t + 15) m. The velocity of the body when its acceleration becomes zero is: (1) 4 m s−1 (2) 8 m s−1 (3) 10 m s−1 (4) 6 m s−1

Q2. A cyclist starts from the point P of a circular ground of radius 2 km and travels along its circumference to the point S. The displacement of a cyclist is: (1) √8 km (2) 8 km (3) 6 km (4) 4 km

Q2. Train A is moving along two parallel rail tracks towards north with 72 km h-1 and train 𝐵 is moving towards south with speed 108 km h-1. Velocity of train 𝐵 with respect to 𝐴 and velocity of ground with respect to 𝐵 are (in m s-1): (1) -30 and 50 (2) -50 and -30 (3) -50 and 30 (4) 50 and -30

Q2. What is the dimensional formula of ab−1 in the equation (P + V2a )(V −b) = RT, where letters have their usual meaning. (1) [M−1 L5 T3] (2) [M6 L7 T4] (3) [ML2 T−2] (4) [M0 L3 T−2]

Q2. Position of an ant ( S in metres) moving in Y −Z plane is given by S = 2t2ˆj + 5ˆk (where t is in second). The magnitude and direction of velocity of the ant at t = 1 s will be : (1) 16 m s−1 in y-direction (2) 4 m s−1 in x-direction (3) 9 m s−1 in z-direction (4) 4 m s−1 in y-direction

Q3. If the radius of curvature of the path of two particles of same mass are in the ratio 3 : 4, then in order to have constant centripetal force, their velocities will be in the ratio of: (1) √3 : 2 (2) 1 : √3 (3) √3 : 1 (4) 2 : √3

Q3. A light string passing over a smooth light fixed pulley connects two blocks of masses 𝑚1 and 𝑚2. If the 𝑔 acceleration of the system is 8, then the ratio of masses is (1) 9 (2) 8 7 1 4 5 (3) (4) 3 3

Q3. A 2 kg brick begins to slide over a surface which is inclined at an angle of 45∘ with respect to horizontal axis. The co-efficient of static friction between their surfaces is: (1) 1.7 (2) 1 √3 (3) 0.5 (4) 1

Q3. Three blocks 𝐴, 𝐵 and 𝐶 are pulled on a horizontal smooth surface by a force of 80 N as shown in figure. The tensions 𝑇1 and 𝑇2 in the string are respectively: (1) 40N, 64N (2) 60N, 80N (3) 88N, 96N (4) 80N, 100N

Q3. A cricket player catches a ball of mass 120 g moving with 25 m s-1 speed. If the catching process is completed in 0 . 1 s then the magnitude of force exerted by the ball on the hand of player will be(in SI unit): (1) 24 (2) 12 (3) 25 (4) 30

Q3. A body of weight 200 N is suspended from a tree branch through a chain of mass 10 kg. The branch pulls the chain by a force equal to (if g = 10 m/s2 ) : (1) 100 N (2) 200 N (3) 300 N (4) 150 N

Q4. Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is : (1) 3 : 5 (2) 5 : 4 (3) 2 : 5 (4) 4 : 5

Q4. A stationary particle breaks into two parts of masses mA and mB which move with velocities vA and vB respectively. The ratio of their kinetic energies (KB : KA) is : (1) vB : vA (2) mB : mA (3) mBvB : mAvA (4) 1 : 1

Q4. A particle is placed at the point A of a frictionless track ABC as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point B is: (Take g = 10 m s−2). (1) 20 m s−1 (2) √10 m s−1 (3) 2√10 m s−1 (4) 10 m s−1

Q4. A heavy box of mass 50 kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is : (1) 1.47 N (2) 147 N (3) 14.7 N (4) 1470 N

Q4. A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the co-efficient of friction between the surfaces is 0. 4 , then the work done against friction (in J) is: (1) 4200 (2) 3900 (3) 4000 (4) 4500

Q4. A thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity ω. If another disc of same dimensions but of mass M/2 is placed gently on the first disc co-axially, then the new angular velocity of the system is : (1) 3 ω (2) 5 ω 2 4 (3) 2 ω (4) 4 ω 3 5

Q4. A body of mass 4 kg experiences two forces →𝐹1 = 5 ^𝑖+ 8 ^𝑗+ 7 ^𝑘 and →𝐹2 = 3 ^𝑖- 4 ^𝑗- 3 ^𝑘. The acceleration acting on the body is: (1) -2 ^𝑖- ^𝑗- ^𝑘 (2) 4 ^𝑖+ 2 ^𝑗+ 2 ^𝑘 (3) 2 ^𝑖+ ^𝑗+ ^𝑘 (4) 2 ^𝑖+ 3 ^𝑗+ 3 ^𝑘

Q5. A body of mass 1000 kg is moving horizontally with a velocity 6 m s−1 . If 200 kg extra mass is added, the final velocity (in m s−1 ) is: (1) 6 (2) 2 (3) 3 (4) 5

Q5. A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be : (1) 1 : 2 (2) √3 : 2 (3) 2 : 1 (4) 1 : 1

Q5. Three bodies A, B and C have equal kinetic energies and their masses are 400 g. 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is : (1) √2; √3; 1 (2) 1 : √3 : 2 (3) 1 : √3 : √2 (4) √3 : √2 : 1

Q5. The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is: (1) 1 : 9 (2) 1 : 3 (3) 1 : 27 (4) 1 : 81