Problem Solving

Q. If the thrust on a rocket moving with a velocity of $300\text{m/s}$ is $210\text{N}$, the rate of combustion of the fuel is

1. $0.007\text{kg/s}$
2. $1.4\text{kg/s}$
3. $0.7\text{kg/s}$
4. $10.7\text{kg/s}$

Q. If F is $200$ N then find acceleration of B.

1. $5m/s^2$
2. $10m/s^2$
3. $4m/s^2$
4. zero

Q. A 1 kg body slides from the point A along a horizontal track with an initial speed of $6m{s}^{-1}$ towards a weightless horizontal spring of length 2 m and force constant $4N{m}^{-1}$.The part AB of the track is frictionless and the part BC has the coefficients of static and dynamic friction 0.22 and 0.2, respectively. Find the total distance through which the block moves before it comes to rest completely ($g=10m{s}^{-2}$),
if AB = 4 m and BD = 4.28 m.

Q. A block of 100 N is sliding down with constant velocity on an inclined plane. The angle of inclination is 7${}^o$. Calculate the force of the friction on the block. (sin 7${}^o$ = 0.12)

1. 0.0012 N
2. 0.07 N
3. 12 N
4. 70 N
5. 100 N

Q. A box of mass 20 kg is kept on a rough horizontal surface ($\mu =0.1$). There is a spring mass system having block of mass 20 kg and spring of spring constant 100 N/m in the box. There is no friction between block and box and spring is initially relaxed. Now, an external force of 120 N is applied on the box. Find the acceleration of the box (in $m/s^2$) just after applying the force.

Q. A $40kg$ slab rests on frictionless floor. A $10kg$ block rests on the top of the slab. The stafic coefficient of friction between block and the slab is $0.60$ while the Kinetic friction is $0.40$. The $10kg$ block is acted upon by a horizontal force of $100N$. If $g=9.8m/s^2$ find the resulting accel. Of the slab $\left(0.98m/s^2\right)$

Q. A smooth block is released at rest from ${45}^{\circ }$ incline slides a distance $d$. The time taken to slide is $n$ time as much to slide on a rough incline plane than on a smooth incline. Find the coefficient of friction.

1. ${\mu }_k=\sqrt{1-\frac{1}{n^2}}$
2. ${\mu }_k=1-\frac{1}{n^2}$
3. ${\mu }_x=1-\frac{1}{n^2}$
4. ${\mu }_x=\sqrt{1-\frac{1}{n^2}}$

Q. The friction coefficient between a road and the tyre of a vehicle is $4/3$. Find the maximum incline the road may have so that once hard brakes are applied and the wheel starts skidding, the vehicle going down at a speed of $36$ km/hr is stopped within $5$m.

Q. Body A in Fig. weighs $102$ N, and body B weighs $32$ N. The coefficients of friction between A and the incline is ${\mu }_s=0.56$ and ${\mu }_k=0.25$. Angle $\theta$ is ${40}^{\circ }$. Let the positive direction of an x-axis be up the incline. In unit-vector notation, what is the acceleration of A if A is initially (a) at rest, (b) moving up the incline, and (c) moving down the incline?

Q. The force of friction acting on a body when velocity is $4m{s}^{-1}$ is $8N$. The force of friction when the velocity is $8m{s}^{-1}$ is

1. 4 N
2. 8 N
3. 16 N
4. 32 N