Laws of Motion
- A ball of mass 0.5 kg is dropped from a height of 40 m. The ball hits the ground and rises to a height of 10 m. The impulse imparted to the ball during its collision with the ground is (Take g = 9.8 m/s^2) Answer: 1. 21 NS Key idea: impulse equals change in momentum, and the velocity direction reverses at the ground. v_before=√(2gh₁)=√(2×9.8×40... 1
- There are two inclined surfaces 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 time to slide down on rough surface than on the smo… Answer: 4. 0.75 Key idea: for a fixed length L starting from rest, L=1/2 a t² , so t∝ 1/sqrt a . Smooth plane: a_s=gsin45^° . Rough plane: a... 1
- A bob is whirled in a horizontal plane by means of a string with an initial speed of ω rpm. The tension in the string is T. If speed becomes 2ω while keeping the same radius, the tension in the string becomes : Answer: 3. 4T Key idea: The tension supplies the centripetal force: T=mω²r . With the same m and r , T∝ω² . Doubling the speed (rpm) gives T... 1
- 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 A on block B is : Answer: 4. 6 N Key idea: Both blocks move together with the same acceleration. Find it first, then use it for block B. a=F/m_A+m_B=10/2+3=2... 1
- Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.15 (g=10 m s^-2). Answer: 4. 1.5 mathrmm s⁻² The body stays at rest relative to the car only while the pseudo-force ma is balanced by static friction, whose m... 1
- A football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is : Answer: 4. along north-east Force is along the change in velocity, vec F∝ Δvec v=vec v_f-vec v_i . Initially the velocity is southward, -vha... 1
- A shell of mass m is at rest initially. It explodes into three fragments having mass in the ratio 2 : 2 : 1. If the fragments having equal mass fly off along mutually perpendicular directions with speed v, the speed of the third (lighter) fragment is… Answer: 4. 2√(2) v The shell is at rest, so total momentum after explosion is zero. Masses are 2m/5,\ 2m/5 and m/5 . The two equal fragments... 1
- A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is (g = 10 m/s^2) nearly : Answer: 2. 4.2 kg m/s Key idea: impulse equals change in momentum; the velocity reverses. Speed at the ground v=√(2gh)=√(200)≈14.1 m/s. Rebo... 1
- Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is : Answer: 3. g/5 Atwood machine: the heavier mass moves down, and both masses share the same acceleration. a=(m₂-m₁)g/m₁+m₂=(6-4)g/6+4=g/5 Ans... 1
- A particle moving with velocity V is acted by three forces shown by the vector triangle PQR. The velocity of the particle will : Answer: 3. remain constant In the figure the three vectors overrightarrowPQ,overrightarrowQR,overrightarrowRP are placed head to tail and fo... 1
- A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to ke… Answer: 3. 10 rad/s The wall's normal force supplies the centripetal force: N=mω²r . Friction balances weight: μ N=mg . μ mω²r=mg⇒ω=√(g/μ r)... 1
- A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and θ for the block to remain stationary on the wedge is Answer: 4. a=gtanθ For the block to stay at rest on the smooth wedge accelerating right with a , in the wedge frame use a pseudo force ma on... 1
- Which one of the following statements is incorrect ? Answer: 4. Coefficient of sliding friction has dimensions of length. Check each statement. Rolling friction is smaller than sliding friction... 1
- One end of string of length l is connected to a particle of mass 'm' and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed 'v', the net force on the particle (directed towards center) w… Answer: 4. T Key idea: only the string tension acts in the horizontal plane. Weight and normal reaction cancel vertically. So the net force... 1
- Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is c… Answer: 1. g/3 , g Key idea: the spring force cannot change instantly, but the string tension vanishes at once. Before cutting, the spring h... 1
- A rigid ball of mass m strikes a rigid wall at 60° and gets reflected without loss of speed as shown in the figure below. The value of impulse imparted by the wall on the ball will be Answer: 4. mV The wall is smooth, so only the component of velocity perpendicular to the wall changes; the parallel component stays the same... 1
- A car is negotiating a curved road of radius R. The road is banked at an angle θ. The coefficient of friction between the tyres of the car and the road is μ_s. The maximum safe velocity on this road is : Answer: 2. √(gRμ_s+tanθ/1-μ_stanθ) Key idea: at maximum speed friction acts down the slope, along with the normal reaction. Vertical: Ncosθ=... 1