An electric lift with a maximum load of $2000\,kg$ (lift + passengers) is moving up with a constant speed of $1.5\,m/s$. The frictional force opposing the motion is $3000\,N$. The minimum power delivered by the motor to the lift in watts is: $(g=10\,m/s^2)$

Two masses $A$ and $B$ of $10\,kg$ and $5\,kg$ respectively are connected by a string passing over a frictionless pulley fixed at the corner of a table. The coefficient of friction between mass $A$ and the table is $0.2$. The minimum mass of $C$ that must be placed on $A$ to prevent it from moving is equal to $...........\,kg$.

$A$ block of mass $5\, kg$ is $(i)$ pushed in case $(A)$ and $(ii)$ pulled in case $(B)$,by a force $F = 20\, N$,making an angle of $30^o$ with the horizontal,as shown in the figures. The coefficient of friction between the block and floor is $\mu = 0.2$. The difference between the accelerations of the block,in case $(B)$ and case $(A)$ will be ........ $ms^{-2}$ .$(g = 10\, ms^{-2})$

$Assertion$: On a rainy day,it is difficult to drive a car or bus at high speed.
$Reason$: The value of the coefficient of friction is lowered due to the wetting of the surface.

$A$ body of mass $3 \, kg$ hits a wall at an angle of $60^\circ$ with the wall and returns at the same angle. The speed of the body is $10 \, m/s$ and the impact time is $0.2 \, s$. Calculate the force exerted on the wall.

Statement $I :$ $A$ cyclist is moving on an unbanked road with a speed of $7 \, km/h$ and takes a sharp circular turn along a path of radius $2 \, m$ without reducing the speed. The static friction coefficient is $0.2$. The cyclist will not slip and pass the curve $(g = 9.8 \, m/s^2)$.
Statement $II :$ If the road is banked at an angle of $45^{\circ}$,the cyclist can cross the curve of $2 \, m$ radius with a speed of $18.5 \, km/h$ without slipping.