$A$ force $F$ is applied on the top of a cube as shown in the figure. The coefficient of friction between the cube and the ground is $\mu$. If $F$ is gradually increased,the cube will topple before sliding. Then the range of $\mu$ is:

At the moment $t=0$, a time-dependent force $F=at$ (where $a$ is a constant equal to $1 \,Ns^{-1}$) is applied to a body of mass $1 \,kg$ resting on a smooth horizontal plane as shown in the figure. If the direction of this force makes an angle $45^{\circ}$ with the horizontal, then the velocity of the body at the moment it leaves the plane is (acceleration due to gravity $=10 \,ms^{-2}$)

$A$ block of mass $m$ is moving with a constant acceleration $a$ on a rough plane. If the coefficient of friction between the block and the ground is $\mu$,the power delivered by the external agent after a time $t$ from the beginning is equal to:

$A$ 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.

For the given system,find the tension $T_2$ in the upper string.

$A$ heavy ball of mass $M$ is suspended from the ceiling of a car by a light string of mass $m$ $(m \ll M)$. When the car is at rest,the speed of transverse waves in the string is $60 \, ms^{-1}$. When the car has acceleration $a$,the wave-speed increases to $60.5 \, ms^{-1}$. The value of $a$,in terms of gravitational acceleration $g$,is closest to: