Two blocks of mass 2 kg and 5 kg are connected by an ideal string passing over a pulley. The block of mass 2 kg is free to slide on a surface inclined at an angle of 30^@with the horizontal whereas 5 kg block hangs freely. Find the acceleration of the system and the tension in the string.

Two blocks of mass 2 kg and 5 kg are connected by an ideal string pass

1.	Two blocks of mass 2 kg and 5 kg are connected by an ideal string passing over a pulley. The block of mass 2 kg is free to slide on a surface inclined at an angle of 30^@with the horizontal whereas 5 kg block hangs freely. Find the acceleration of the system and the tension in the string.
Answer» <html><body><p></p>Solution :<img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/FM_PHY_XI_V01_C03_E02_156_S01.png" width="80%"/> <br/>Let a be the acceleration of the <a href="https://interviewquestions.tuteehub.com/tag/system-1237255" style="font-weight:bold;" target="_blank" title="Click to know more about SYSTEM">SYSTEM</a> and T be the <a href="https://interviewquestions.tuteehub.com/tag/tension-1241727" style="font-weight:bold;" target="_blank" title="Click to know more about TENSION">TENSION</a> in the string. Equations of motions for 5 kg and 2 kg blocks are 5g - T = 5a...(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>) <br/> `T =2 g sin theta - f = 2a`...(2) <br/> where f= force of limiting friction <br/> `mu R = mu mg cos theta = 0.3 xx 2 g xx cos 30^@` <br/> <a href="https://interviewquestions.tuteehub.com/tag/solving-1217196" style="font-weight:bold;" target="_blank" title="Click to know more about SOLVING">SOLVING</a> (1) and (2) <br/> `a = 4.87 m//s^2` <br/> `T = 24.65 N`</body></html>